Approximation algorithms for homogeneous polynomial optimization with quadratic constraints

In this paper, we consider approximation algorithms for optimizing a generic multi-variate homogeneous polynomial function, subject to homogeneous quadratic constraints. Such optimization models have wide applications, e.g., in signal processing, magnetic resonance imaging (MRI), data training, appr...

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Published in:	Mathematical programming Vol. 125; no. 2; pp. 353 - 383
Main Authors:	He, Simai, Li, Zhening, Zhang, Shuzhong
Format:	Journal Article Conference Proceeding
Language:	English
Published:	Berlin/Heidelberg Springer-Verlag 01.10.2010 Springer Springer Nature B.V
Subjects:	Algorithms Applied sciences Approximation Calculus of Variations and Optimal Control; Optimization Combinatorics Ellipsoids Exact sciences and technology Full Length Paper Intersections Linear algebra Magnetic resonance imaging Mathematical analysis Mathematical and Computational Physics Mathematical Methods in Physics Mathematical models Mathematical programming Mathematics Mathematics and Statistics Mathematics of Computing Maximization Numerical Analysis Operational research and scientific management Operational research. Management science Optimization Polynomials Quantum physics Signal processing Studies Theoretical Voice recognition Multi-linear tensor form 90C26 90C59 15A69 Approximation algorithm Polynomial function optimization Intersection Non convex programming Linear form Polynomial approximation Worst case method Constraint satisfaction Polynomial method Modeling Convex programming Sphere Portfolio selection Convex function Approximation theory Cartesian product Mathematical programming Quadratic programming Set constraint Nuclear magnetic resonance imaging Constrained optimization Polynomial time Polynomial function NP hard problem Signal processing Homogeneous function Ellipsoid Portfolio management Non convex analysis
ISSN:	0025-5610, 1436-4646
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Abstract	In this paper, we consider approximation algorithms for optimizing a generic multi-variate homogeneous polynomial function, subject to homogeneous quadratic constraints. Such optimization models have wide applications, e.g., in signal processing, magnetic resonance imaging (MRI), data training, approximation theory, and portfolio selection. Since polynomial functions are non-convex, the problems under consideration are all NP-hard in general. In this paper we shall focus on polynomial-time approximation algorithms. In particular, we first study optimization of a multi-linear tensor function over the Cartesian product of spheres. We shall propose approximation algorithms for such problem and derive worst-case performance ratios, which are shown to be dependent only on the dimensions of the model. The methods are then extended to optimize a generic multi-variate homogeneous polynomial function with spherical constraint. Likewise, approximation algorithms are proposed with provable approximation performance ratios. Furthermore, the constraint set is relaxed to be an intersection of co-centered ellipsoids; namely, we consider maximization of a homogeneous polynomial over the intersection of ellipsoids centered at the origin, and propose polynomial-time approximation algorithms with provable worst-case performance ratios. Numerical results are reported, illustrating the effectiveness of the approximation algorithms studied.
AbstractList	Issue Title: 20th International Symposium on Mathematical Programming - ISMP 2009 In this paper, we consider approximation algorithms for optimizing a generic multi-variate homogeneous polynomial function, subject to homogeneous quadratic constraints. Such optimization models have wide applications, e.g., in signal processing, magnetic resonance imaging (MRI), data training, approximation theory, and portfolio selection. Since polynomial functions are non-convex, the problems under consideration are all NP-hard in general. In this paper we shall focus on polynomial-time approximation algorithms. In particular, we first study optimization of a multi-linear tensor function over the Cartesian product of spheres. We shall propose approximation algorithms for such problem and derive worst-case performance ratios, which are shown to be dependent only on the dimensions of the model. The methods are then extended to optimize a generic multi-variate homogeneous polynomial function with spherical constraint. Likewise, approximation algorithms are proposed with provable approximation performance ratios. Furthermore, the constraint set is relaxed to be an intersection of co-centered ellipsoids; namely, we consider maximization of a homogeneous polynomial over the intersection of ellipsoids centered at the origin, and propose polynomial-time approximation algorithms with provable worst-case performance ratios. Numerical results are reported, illustrating the effectiveness of the approximation algorithms studied.[PUBLICATION ABSTRACT] In this paper, we consider approximation algorithms for optimizing a generic multi-variate homogeneous polynomial function, subject to homogeneous quadratic constraints. Such optimization models have wide applications, e.g., in signal processing, magnetic resonance imaging (MRI), data training, approximation theory, and portfolio selection. Since polynomial functions are non-convex, the problems under consideration are all NP-hard in general. In this paper we shall focus on polynomial-time approximation algorithms. In particular, we first study optimization of a multi-linear tensor function over the Cartesian product of spheres. We shall propose approximation algorithms for such problem and derive worst-case performance ratios, which are shown to be dependent only on the dimensions of the model. The methods are then extended to optimize a generic multi-variate homogeneous polynomial function with spherical constraint. Likewise, approximation algorithms are proposed with provable approximation performance ratios. Furthermore, the constraint set is relaxed to be an intersection of co-centered ellipsoids; namely, we consider maximization of a homogeneous polynomial over the intersection of ellipsoids centered at the origin, and propose polynomial-time approximation algorithms with provable worst-case performance ratios. Numerical results are reported, illustrating the effectiveness of the approximation algorithms studied.
Author	He, Simai Li, Zhening Zhang, Shuzhong
Author_xml	– sequence: 1 givenname: Simai surname: He fullname: He, Simai organization: Department of Management Sciences, City University of Hong Kong – sequence: 2 givenname: Zhening surname: Li fullname: Li, Zhening organization: Department of Systems Engineering and Engineering Management, The Chinese University of Hong Kong – sequence: 3 givenname: Shuzhong surname: Zhang fullname: Zhang, Shuzhong email: zhang@se.cuhk.edu.hk organization: Department of Systems Engineering and Engineering Management, The Chinese University of Hong Kong
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Cites_doi	10.1007/s10898-004-6875-1 10.1007/s101070050100 10.1137/090772952 10.1137/S1052623403420857 10.1007/s10898-007-9224-3 10.1109/TSP.2002.808112 10.1007/978-1-4757-3216-0_17 10.1090/S0002-9947-01-02898-7 10.1080/10556789908805762 10.1145/779359.779363 10.1137/080729104 10.1137/050642691 10.1007/s10107-003-0387-5 10.1109/TAC.2008.923679 10.1016/B978-075065448-7.50011-2 10.1287/moor.1080.0326 10.1007/s10107980012a 10.1080/10556780802699201 10.1016/j.tcs.2006.05.011 10.1137/S0895479801387413 10.1145/780542.780545 10.1016/S0377-0427(00)00385-X 10.1137/S1052623403421498 10.1137/04061341X 10.1023/A:1024778309049 10.1007/s00365-006-0639-2 10.1137/1.9780898718829 10.1007/s101070050006 10.1023/A:1008370723217 10.1016/S0378-4266(02)00261-3 10.1080/10556789808805690 10.1016/j.jsc.2005.05.007 10.1007/978-3-540-73273-0_26 10.1007/s10100-007-0052-9 10.1137/070679041 10.1111/j.1354-7798.2006.00309.x 10.1016/j.laa.2006.08.026 10.1016/j.ijplas.2007.07.016 10.1016/j.jmaa.2006.02.071 10.1145/227683.227684 10.1137/S1052623400366802 10.1080/10556789908805766 10.1016/j.jat.2007.08.005 10.1007/11751595_95
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Keywords	Multi-linear tensor form 90C26 90C59 15A69 Approximation algorithm Polynomial function optimization Intersection Non convex programming Linear form Polynomial approximation Worst case method Constraint satisfaction Polynomial method Modeling Convex programming Sphere Portfolio selection Convex function Approximation theory Cartesian product Mathematical programming Quadratic programming Set constraint Nuclear magnetic resonance imaging Constrained optimization Polynomial time Polynomial function NP hard problem Signal processing Homogeneous function Ellipsoid Portfolio management Non convex analysis
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References	PrakashA.J.ChangC.H.PactwaT.E.Selecting a portfolio with skewness: recent evidence from US, European, and Latin American equity marketsJ Banking Financ.2003271375139010.1016/S0378-4266(02)00261-3 SoA.M.C.YeY.ZhangJ.A unified theorem on SDP rank reductionMath. Oper. Res.20083391092010.1287/moor.1080.03262464650 Gurvits, L.: Classical deterministic complexity of Edmonds’ problem and quantum entanglement. In: Proceedings of the Thirty-Fifth ACM Symposium on Theory of Computing, pp. 10–19, ACM, New York (2003) MandelbrotB.HudsonR.L.The (Mis)Behavior of Markets2004New YorkBasic Books1140.91004 Ghosh, A., Tsigaridas, E., Descoteaux, M., Comon, P., Mourrain, B., Deriche, R.: A polynomial based approach to extract the maxima of an antipodally symmetric spherical function and its application to extract fiber directions from the orientation distribution function in diffusion MRI. Computational Diffusion MRI Workshop (CDMRI’08), New York (2008) Parrilo, P.A.: Structured semidefinite programs and semialgebraic geometry methods in robustness and optimization. PhD Dissertation, California Institute of Technology, CA (2000) LuoZ.Q.SturmJ.F.ZhangS.Multivariate nonnegative quadratic mappingsSIAM J. Optim.200414114011621069.1501910.1137/S10526234034214982112968 GoemansM.X.WilliamsonD.P.Improved approximation algorithms for maximum cut and satisfiability problems using semidefinite programmingJ. ACM199542111511450885.6808810.1145/227683.2276841412228 De KlerkE.The complexity of optimizing over a simplex, hypercube or sphere: a short surveyCentral Eur J. Oper. Res.2008161111251152.9060710.1007/s10100-007-0052-92407041 QiL.WanZ.YangY.F.Global minimization of normal quadratic polynomials based on global descent directionsSIAM J. Optim.2004152753021077.9006610.1137/S10526234034208572112986 SturmJ.F.SeDuMi 1.02, a Matlab toolbox for optimization over symmetric conesOptim. Methods Softw.199911&1262565310.1080/105567899088057661778433 De AthaydeG.M.FlôresR.G.Jr.SatchellS.ScowcroftA.Incorporating skewness and kurtosis in portfolio optimization: a multidimensional efficient set, 10Advances in Portfolio Construction and Implementation2003UKButterworth-Heinemann24325710.1016/B978-075065448-7.50011-2 MaringerD.ParpasP.Global optimization of higher order moments in portfolio selectionJ. Glob. Optim.2009432192301169.9045410.1007/s10898-007-9224-32471883 NesterovYu.Semidefinite relaxation and nonconvex quadratic optimizationOptim. Methods Softw.199891411600904.9013610.1080/105567898088056901618100 QiL.Eigenvalues and invariants of tensorsJ. Math. Anal. Appl.2007325136313771113.1502010.1016/j.jmaa.2006.02.0712270090 ZhangS.HuangY.Complex quadratic optimization and semidefinite programmingSIAM J. Optim.2006168718901113.9011510.1137/04061341X2197560 LuoZ.Q.SidiropoulosN.D.TsengP.ZhangS.Approximation bounds for quadratic optimization with homogeneous quadratic constraintsSIAM J. Optim.2007181281156.900112299671 KroóA.SzabadosJ.Joackson-type theorems in homogeneous approximationJ. Appr. Theory20081521191142.4100310.1016/j.jat.2007.08.005 KofidisE.RegaliaPh.On the best rank-1 approximation of higher order supersymmetric tensorsSIAM J. Matrix Anal. App.2002238638841001.6503510.1137/S08954798013874131896822 LuoZ.Q.ZhangS.A semidefinite relaxation scheme for multivariate quartic polynomial optimization with quadratic constraintsSIAM J. Optim.2010201716173610.1137/0907729522600236 MaricicB.LuoZ.Q.DavidsonT.N.Blind constant modulus equalization via convex optimizationIEEE Trans. Signal Process.20035180581810.1109/TSP.2002.8081121963878 NesterovYu.FrenkJ.B.G.Squared functional systems and optimization problemsHigh Performance Optimization2000DordrechtKluwer Academic Press405440 YeY.Approximating global quadratic optimization with convex quadratic constraintsJ. Glob. Optim.1999151170953.9004010.1023/A:1008370723217 Grant, M., Boyd, S.: CVX: Matlab Software for Disciplined Convex Programming, version 1.2. http://cvxr.com/cvx (2010) NiQ.QiL.WangF.An eigenvalue method for testing positive definiteness of a multivariate formIEEE Trans. Automat. Contr.2008531096110710.1109/TAC.2008.9236792445667 Nesterov, Yu.: Random walk in a simplex and quadratic optimization over convex polytopes. CORE Discussion Paper. UCL, Louvain-la-Neuve, Belgium (2003) JondeauE.RockingerM.Optimal portfolio allocation under higher momentsEur. Financ. Manage.200612295510.1111/j.1354-7798.2006.00309.x LaurentM.PutinarM.SullivantS.Sums of squares, moment matrices and optimization over polynomialsEmerging Applications of Algebraic Geometry, Series: The IMA Volumes in Mathematics and its Applications, vol. 1492009BerlinSpringer QiL.TeoK.L.Multivariate polynomial minimization and its applications in signal processingJ. Glob. Optim.2003264194331023.9006410.1023/A:10247783090491989748 LasserreJ.B.Polynomials nonnegative on a grid and discrete representationsTrans. Am. Math. Soc.200135463164910.1090/S0002-9947-01-02898-71862561 Barmpoutis, A., Jian, B., Vemuri, B.C., Shepherd, T.M.: Symmetric positive 4th order tensors and their estimation from diffusion weighted MRI. In: Karssemijer, N., Lelieveldt, B. (eds.) IPMI 2007, LNCS 4584, pp. 308–319 (2007) LasserreJ.B.Global optimization with polynomials and the problem of momentsSIAM J. Optim.2001117968171010.9006110.1137/S10526234003668021814045 De KlerkE.LaurentM.ParriloP.A.A PTAS for the minimization of polynomials of fixed degree over the simplexTheor. Comput. Sci.200626121022510.1016/j.tcs.2006.05.0112252579 Fujisawa, K., Kojima, M., Nakata, K., Yamashita, M.: SDPA (SemiDefinite Programming Algorithm) User’s Manual—version 6.2.0, Research Report B-308, Department of Mathematical and Computing Sciences, Tokyo Institute of Technology, Japan (1995) HenrionD.LasserreJ.B.GloptiPoly: global optimization over polynomials with Matlab and SeDuMiACM Tran. Math. Soft2003291651941070.6554910.1145/779359.7793632000881 Parpas, P., Rustem, B.: Global optimization of the scenario generation and portfolio selection problems. ICCSA 2006, LNCS 3982, pp. 908–917 (2006) ZhangS.Quadratic maximization and semidefinite relaxationMath. Prog. A2000874534651009.9008010.1007/s101070050006 HenrionD.LasserreJ.B.LoefbergJ.GloptiPoly 3: moments, optimization and semidefinite programmingOptim. Methods Softw.2009247617791178.9027710.1080/105567808026992012554910 QiL.Eigenvalues of a real supersymmetric tensorJ. Symbolic Comput.200540130213241125.1501410.1016/j.jsc.2005.05.0072178089 ZhangX.QiL.YeY.The cubic spherical optimization problems, Working Paper2009Hong KongThe Hong Kong Polytechnic University YeY.Approximating quadratic programming with bound and quadratic constraintsMath. Prog.1999842192260971.90056 MicchelliC.A.OlsenP.Penalized maximum-likelihood estimation, the Baum-Welch algorithm, diagonal balancing of symmetric matrices and applications to training acoustic dataJ. Comput. Appl. Math.20001193013310962.6500810.1016/S0377-0427(00)00385-X1774224 TohK.C.ToddM.J.TutuncuR.H.SDPT3—a Matlab software package for semidefinite programmingOptim. Methods Softw.19991154558110.1080/105567899088057621778429 DahlG.LeinaasJ.M.MyrheimJ.OvrumE.A tensor product matrix approximation problem in quantum physicsLinear. Algebra. Appl.20074207117251118.1502710.1016/j.laa.2006.08.0262278245 NemirovskiA.RoosC.TerlakyT.On maximization of quadratic form over intersection of ellipsoids with common centerMath. Prog. A1999864634730944.9005610.1007/s1010700501001733748 VarjúP.P.Approximation by homogeneous polynomialsConst. Appr.2007263173371126.4100410.1007/s00365-006-0639-2 Ben-TalA.NemirovskiA.Lectures on Modern Convex Optimization: Analysis, Algorithms, and Engineering Applications2001PhiladelphiaMPS-SIAM Series on Optimization0986.90032 LingC.NieJ.QiL.YeY.Biquadratic optimization over unit spheres and semidefinite programming relaxationsSIAM J. Optim.200920128613100577937810.1137/0807291042546345 ParriloP.A.Semidefinite programming relaxations for semialgebraic problemsMath. Prog. B2003962933201043.1401810.1007/s10107-003-0387-51993050 QiL.Extrema of a real polynomialJ. Glob. Optim.2004304054331082.9009110.1007/s10898-004-6875-1 HeS.LuoZ.Q.NieJ.ZhangS.Semidefinite relaxation bounds for indefinite homogeneous quadratic optimizationSIAM J. Optim.2008195035231180.9021810.1137/0706790412425027 SoareS.YoonJ.W.CazacuO.On the use of homogeneous polynomials to develop anisotropic yield functions with applications to sheet formingInt. J. Plast.2008249159440527440510.1016/j.ijplas.2007.07.016 E. De Klerk (409_CR6) 2006; 261 E. Kofidis (409_CR16) 2002; 23 L. Qi (409_CR41) 2003; 26 C.A. Micchelli (409_CR28) 2000; 119 J.B. Lasserre (409_CR19) 2001; 354 A.M.C. So (409_CR43) 2008; 33 409_CR10 409_CR11 Z.Q. Luo (409_CR24) 2010; 20 D. Maringer (409_CR27) 2009; 43 A.J. Prakash (409_CR37) 2003; 27 Z.Q. Luo (409_CR22) 2007; 18 K.C. Toh (409_CR46) 1999; 11 E. Jondeau (409_CR15) 2006; 12 Z.Q. Luo (409_CR23) 2004; 14 X. Zhang (409_CR52) 2009 P.P. Varjú (409_CR47) 2007; 26 S. Zhang (409_CR51) 2006; 16 L. Qi (409_CR38) 2004; 30 Y. Ye (409_CR49) 1999; 15 L. Qi (409_CR40) 2007; 325 A. Ben-Tal (409_CR2) 2001 J.F. Sturm (409_CR45) 1999; 11&12 G.M. De Athayde (409_CR4) 2003 E. De Klerk (409_CR5) 2008; 16 A. Kroó (409_CR17) 2008; 152 P.A. Parrilo (409_CR36) 2003; 96 M. Laurent (409_CR20) 2009 B. Mandelbrot (409_CR25) 2004 C. Ling (409_CR21) 2009; 20 S. He (409_CR12) 2008; 19 409_CR34 Yu. Nesterov (409_CR31) 2000 409_CR35 409_CR32 L. Qi (409_CR42) 2004; 15 409_CR7 409_CR8 409_CR1 M.X. Goemans (409_CR9) 1995; 42 Yu. Nesterov (409_CR30) 1998; 9 L. Qi (409_CR39) 2005; 40 D. Henrion (409_CR14) 2009; 24 S. Zhang (409_CR50) 2000; 87 D. Henrion (409_CR13) 2003; 29 G. Dahl (409_CR3) 2007; 420 S. Soare (409_CR44) 2008; 24 A. Nemirovski (409_CR29) 1999; 86 Q. Ni (409_CR33) 2008; 53 J.B. Lasserre (409_CR18) 2001; 11 B. Maricic (409_CR26) 2003; 51 Y. Ye (409_CR48) 1999; 84
References_xml	– reference: NiQ.QiL.WangF.An eigenvalue method for testing positive definiteness of a multivariate formIEEE Trans. Automat. Contr.2008531096110710.1109/TAC.2008.9236792445667 – reference: JondeauE.RockingerM.Optimal portfolio allocation under higher momentsEur. Financ. Manage.200612295510.1111/j.1354-7798.2006.00309.x – reference: VarjúP.P.Approximation by homogeneous polynomialsConst. Appr.2007263173371126.4100410.1007/s00365-006-0639-2 – reference: GoemansM.X.WilliamsonD.P.Improved approximation algorithms for maximum cut and satisfiability problems using semidefinite programmingJ. ACM199542111511450885.6808810.1145/227683.2276841412228 – reference: ParriloP.A.Semidefinite programming relaxations for semialgebraic problemsMath. Prog. B2003962933201043.1401810.1007/s10107-003-0387-51993050 – reference: Ben-TalA.NemirovskiA.Lectures on Modern Convex Optimization: Analysis, Algorithms, and Engineering Applications2001PhiladelphiaMPS-SIAM Series on Optimization0986.90032 – reference: LaurentM.PutinarM.SullivantS.Sums of squares, moment matrices and optimization over polynomialsEmerging Applications of Algebraic Geometry, Series: The IMA Volumes in Mathematics and its Applications, vol. 1492009BerlinSpringer – reference: De KlerkE.LaurentM.ParriloP.A.A PTAS for the minimization of polynomials of fixed degree over the simplexTheor. Comput. Sci.200626121022510.1016/j.tcs.2006.05.0112252579 – reference: QiL.Eigenvalues of a real supersymmetric tensorJ. Symbolic Comput.200540130213241125.1501410.1016/j.jsc.2005.05.0072178089 – reference: Ghosh, A., Tsigaridas, E., Descoteaux, M., Comon, P., Mourrain, B., Deriche, R.: A polynomial based approach to extract the maxima of an antipodally symmetric spherical function and its application to extract fiber directions from the orientation distribution function in diffusion MRI. Computational Diffusion MRI Workshop (CDMRI’08), New York (2008) – reference: QiL.Eigenvalues and invariants of tensorsJ. Math. Anal. Appl.2007325136313771113.1502010.1016/j.jmaa.2006.02.0712270090 – reference: HeS.LuoZ.Q.NieJ.ZhangS.Semidefinite relaxation bounds for indefinite homogeneous quadratic optimizationSIAM J. Optim.2008195035231180.9021810.1137/0706790412425027 – reference: LasserreJ.B.Polynomials nonnegative on a grid and discrete representationsTrans. Am. Math. Soc.200135463164910.1090/S0002-9947-01-02898-71862561 – reference: YeY.Approximating global quadratic optimization with convex quadratic constraintsJ. Glob. Optim.1999151170953.9004010.1023/A:1008370723217 – reference: HenrionD.LasserreJ.B.GloptiPoly: global optimization over polynomials with Matlab and SeDuMiACM Tran. Math. Soft2003291651941070.6554910.1145/779359.7793632000881 – reference: QiL.Extrema of a real polynomialJ. Glob. Optim.2004304054331082.9009110.1007/s10898-004-6875-1 – reference: TohK.C.ToddM.J.TutuncuR.H.SDPT3—a Matlab software package for semidefinite programmingOptim. Methods Softw.19991154558110.1080/105567899088057621778429 – reference: ZhangS.Quadratic maximization and semidefinite relaxationMath. Prog. A2000874534651009.9008010.1007/s101070050006 – reference: DahlG.LeinaasJ.M.MyrheimJ.OvrumE.A tensor product matrix approximation problem in quantum physicsLinear. Algebra. Appl.20074207117251118.1502710.1016/j.laa.2006.08.0262278245 – reference: De KlerkE.The complexity of optimizing over a simplex, hypercube or sphere: a short surveyCentral Eur J. Oper. Res.2008161111251152.9060710.1007/s10100-007-0052-92407041 – reference: NesterovYu.FrenkJ.B.G.Squared functional systems and optimization problemsHigh Performance Optimization2000DordrechtKluwer Academic Press405440 – reference: MaricicB.LuoZ.Q.DavidsonT.N.Blind constant modulus equalization via convex optimizationIEEE Trans. Signal Process.20035180581810.1109/TSP.2002.8081121963878 – reference: Parrilo, P.A.: Structured semidefinite programs and semialgebraic geometry methods in robustness and optimization. PhD Dissertation, California Institute of Technology, CA (2000) – reference: YeY.Approximating quadratic programming with bound and quadratic constraintsMath. Prog.1999842192260971.90056 – reference: MandelbrotB.HudsonR.L.The (Mis)Behavior of Markets2004New YorkBasic Books1140.91004 – reference: SturmJ.F.SeDuMi 1.02, a Matlab toolbox for optimization over symmetric conesOptim. Methods Softw.199911&1262565310.1080/105567899088057661778433 – reference: QiL.WanZ.YangY.F.Global minimization of normal quadratic polynomials based on global descent directionsSIAM J. Optim.2004152753021077.9006610.1137/S10526234034208572112986 – reference: Fujisawa, K., Kojima, M., Nakata, K., Yamashita, M.: SDPA (SemiDefinite Programming Algorithm) User’s Manual—version 6.2.0, Research Report B-308, Department of Mathematical and Computing Sciences, Tokyo Institute of Technology, Japan (1995) – reference: Nesterov, Yu.: Random walk in a simplex and quadratic optimization over convex polytopes. CORE Discussion Paper. UCL, Louvain-la-Neuve, Belgium (2003) – reference: QiL.TeoK.L.Multivariate polynomial minimization and its applications in signal processingJ. Glob. Optim.2003264194331023.9006410.1023/A:10247783090491989748 – reference: NemirovskiA.RoosC.TerlakyT.On maximization of quadratic form over intersection of ellipsoids with common centerMath. Prog. A1999864634730944.9005610.1007/s1010700501001733748 – reference: SoA.M.C.YeY.ZhangJ.A unified theorem on SDP rank reductionMath. Oper. Res.20083391092010.1287/moor.1080.03262464650 – reference: ZhangS.HuangY.Complex quadratic optimization and semidefinite programmingSIAM J. Optim.2006168718901113.9011510.1137/04061341X2197560 – reference: LingC.NieJ.QiL.YeY.Biquadratic optimization over unit spheres and semidefinite programming relaxationsSIAM J. Optim.200920128613100577937810.1137/0807291042546345 – reference: MaringerD.ParpasP.Global optimization of higher order moments in portfolio selectionJ. Glob. Optim.2009432192301169.9045410.1007/s10898-007-9224-32471883 – reference: Grant, M., Boyd, S.: CVX: Matlab Software for Disciplined Convex Programming, version 1.2. http://cvxr.com/cvx (2010) – reference: KroóA.SzabadosJ.Joackson-type theorems in homogeneous approximationJ. Appr. Theory20081521191142.4100310.1016/j.jat.2007.08.005 – reference: LuoZ.Q.SturmJ.F.ZhangS.Multivariate nonnegative quadratic mappingsSIAM J. Optim.200414114011621069.1501910.1137/S10526234034214982112968 – reference: KofidisE.RegaliaPh.On the best rank-1 approximation of higher order supersymmetric tensorsSIAM J. Matrix Anal. App.2002238638841001.6503510.1137/S08954798013874131896822 – reference: Parpas, P., Rustem, B.: Global optimization of the scenario generation and portfolio selection problems. ICCSA 2006, LNCS 3982, pp. 908–917 (2006) – reference: LasserreJ.B.Global optimization with polynomials and the problem of momentsSIAM J. Optim.2001117968171010.9006110.1137/S10526234003668021814045 – reference: De AthaydeG.M.FlôresR.G.Jr.SatchellS.ScowcroftA.Incorporating skewness and kurtosis in portfolio optimization: a multidimensional efficient set, 10Advances in Portfolio Construction and Implementation2003UKButterworth-Heinemann24325710.1016/B978-075065448-7.50011-2 – reference: LuoZ.Q.ZhangS.A semidefinite relaxation scheme for multivariate quartic polynomial optimization with quadratic constraintsSIAM J. Optim.2010201716173610.1137/0907729522600236 – reference: Barmpoutis, A., Jian, B., Vemuri, B.C., Shepherd, T.M.: Symmetric positive 4th order tensors and their estimation from diffusion weighted MRI. In: Karssemijer, N., Lelieveldt, B. (eds.) IPMI 2007, LNCS 4584, pp. 308–319 (2007) – reference: NesterovYu.Semidefinite relaxation and nonconvex quadratic optimizationOptim. Methods Softw.199891411600904.9013610.1080/105567898088056901618100 – reference: SoareS.YoonJ.W.CazacuO.On the use of homogeneous polynomials to develop anisotropic yield functions with applications to sheet formingInt. J. Plast.2008249159440527440510.1016/j.ijplas.2007.07.016 – reference: PrakashA.J.ChangC.H.PactwaT.E.Selecting a portfolio with skewness: recent evidence from US, European, and Latin American equity marketsJ Banking Financ.2003271375139010.1016/S0378-4266(02)00261-3 – reference: MicchelliC.A.OlsenP.Penalized maximum-likelihood estimation, the Baum-Welch algorithm, diagonal balancing of symmetric matrices and applications to training acoustic dataJ. Comput. Appl. Math.20001193013310962.6500810.1016/S0377-0427(00)00385-X1774224 – reference: LuoZ.Q.SidiropoulosN.D.TsengP.ZhangS.Approximation bounds for quadratic optimization with homogeneous quadratic constraintsSIAM J. Optim.2007181281156.900112299671 – reference: Gurvits, L.: Classical deterministic complexity of Edmonds’ problem and quantum entanglement. In: Proceedings of the Thirty-Fifth ACM Symposium on Theory of Computing, pp. 10–19, ACM, New York (2003) – reference: HenrionD.LasserreJ.B.LoefbergJ.GloptiPoly 3: moments, optimization and semidefinite programmingOptim. Methods Softw.2009247617791178.9027710.1080/105567808026992012554910 – reference: ZhangX.QiL.YeY.The cubic spherical optimization problems, Working Paper2009Hong KongThe Hong Kong Polytechnic University – volume: 30 start-page: 405 year: 2004 ident: 409_CR38 publication-title: J. Glob. Optim. doi: 10.1007/s10898-004-6875-1 – volume-title: Emerging Applications of Algebraic Geometry, Series: The IMA Volumes in Mathematics and its Applications, vol. 149 year: 2009 ident: 409_CR20 – volume: 86 start-page: 463 year: 1999 ident: 409_CR29 publication-title: Math. Prog. A doi: 10.1007/s101070050100 – volume: 20 start-page: 1716 year: 2010 ident: 409_CR24 publication-title: SIAM J. Optim. doi: 10.1137/090772952 – volume: 15 start-page: 275 year: 2004 ident: 409_CR42 publication-title: SIAM J. Optim. doi: 10.1137/S1052623403420857 – volume: 43 start-page: 219 year: 2009 ident: 409_CR27 publication-title: J. Glob. Optim. doi: 10.1007/s10898-007-9224-3 – volume: 51 start-page: 805 year: 2003 ident: 409_CR26 publication-title: IEEE Trans. Signal Process. doi: 10.1109/TSP.2002.808112 – start-page: 405 volume-title: High Performance Optimization year: 2000 ident: 409_CR31 doi: 10.1007/978-1-4757-3216-0_17 – volume: 354 start-page: 631 year: 2001 ident: 409_CR19 publication-title: Trans. Am. Math. Soc. doi: 10.1090/S0002-9947-01-02898-7 – volume: 11 start-page: 545 year: 1999 ident: 409_CR46 publication-title: Optim. Methods Softw. doi: 10.1080/10556789908805762 – volume: 29 start-page: 165 year: 2003 ident: 409_CR13 publication-title: ACM Tran. Math. Soft doi: 10.1145/779359.779363 – volume: 20 start-page: 1286 year: 2009 ident: 409_CR21 publication-title: SIAM J. Optim. doi: 10.1137/080729104 – ident: 409_CR35 – volume: 18 start-page: 1 year: 2007 ident: 409_CR22 publication-title: SIAM J. Optim. doi: 10.1137/050642691 – ident: 409_CR7 – volume: 96 start-page: 293 year: 2003 ident: 409_CR36 publication-title: Math. Prog. B doi: 10.1007/s10107-003-0387-5 – volume: 53 start-page: 1096 year: 2008 ident: 409_CR33 publication-title: IEEE Trans. Automat. Contr. doi: 10.1109/TAC.2008.923679 – start-page: 243 volume-title: Advances in Portfolio Construction and Implementation year: 2003 ident: 409_CR4 doi: 10.1016/B978-075065448-7.50011-2 – ident: 409_CR32 – volume: 33 start-page: 910 year: 2008 ident: 409_CR43 publication-title: Math. Oper. Res. doi: 10.1287/moor.1080.0326 – volume: 84 start-page: 219 year: 1999 ident: 409_CR48 publication-title: Math. Prog. doi: 10.1007/s10107980012a – volume: 24 start-page: 761 year: 2009 ident: 409_CR14 publication-title: Optim. Methods Softw. doi: 10.1080/10556780802699201 – volume: 261 start-page: 210 year: 2006 ident: 409_CR6 publication-title: Theor. Comput. Sci. doi: 10.1016/j.tcs.2006.05.011 – volume: 23 start-page: 863 year: 2002 ident: 409_CR16 publication-title: SIAM J. Matrix Anal. App. doi: 10.1137/S0895479801387413 – ident: 409_CR8 – ident: 409_CR11 doi: 10.1145/780542.780545 – volume: 119 start-page: 301 year: 2000 ident: 409_CR28 publication-title: J. Comput. Appl. Math. doi: 10.1016/S0377-0427(00)00385-X – volume: 14 start-page: 1140 year: 2004 ident: 409_CR23 publication-title: SIAM J. Optim. doi: 10.1137/S1052623403421498 – volume: 16 start-page: 871 year: 2006 ident: 409_CR51 publication-title: SIAM J. Optim. doi: 10.1137/04061341X – volume: 26 start-page: 419 year: 2003 ident: 409_CR41 publication-title: J. Glob. Optim. doi: 10.1023/A:1024778309049 – volume: 26 start-page: 317 year: 2007 ident: 409_CR47 publication-title: Const. Appr. doi: 10.1007/s00365-006-0639-2 – volume-title: The cubic spherical optimization problems, Working Paper year: 2009 ident: 409_CR52 – volume-title: Lectures on Modern Convex Optimization: Analysis, Algorithms, and Engineering Applications year: 2001 ident: 409_CR2 doi: 10.1137/1.9780898718829 – volume: 87 start-page: 453 year: 2000 ident: 409_CR50 publication-title: Math. Prog. A doi: 10.1007/s101070050006 – volume: 15 start-page: 1 year: 1999 ident: 409_CR49 publication-title: J. Glob. Optim. doi: 10.1023/A:1008370723217 – volume-title: The (Mis)Behavior of Markets year: 2004 ident: 409_CR25 – volume: 27 start-page: 1375 year: 2003 ident: 409_CR37 publication-title: J Banking Financ. doi: 10.1016/S0378-4266(02)00261-3 – ident: 409_CR10 – volume: 9 start-page: 141 year: 1998 ident: 409_CR30 publication-title: Optim. Methods Softw. doi: 10.1080/10556789808805690 – volume: 40 start-page: 1302 year: 2005 ident: 409_CR39 publication-title: J. Symbolic Comput. doi: 10.1016/j.jsc.2005.05.007 – ident: 409_CR1 doi: 10.1007/978-3-540-73273-0_26 – volume: 16 start-page: 111 year: 2008 ident: 409_CR5 publication-title: Central Eur J. Oper. Res. doi: 10.1007/s10100-007-0052-9 – volume: 19 start-page: 503 year: 2008 ident: 409_CR12 publication-title: SIAM J. Optim. doi: 10.1137/070679041 – volume: 12 start-page: 29 year: 2006 ident: 409_CR15 publication-title: Eur. Financ. Manage. doi: 10.1111/j.1354-7798.2006.00309.x – volume: 420 start-page: 711 year: 2007 ident: 409_CR3 publication-title: Linear. Algebra. Appl. doi: 10.1016/j.laa.2006.08.026 – volume: 24 start-page: 915 year: 2008 ident: 409_CR44 publication-title: Int. J. Plast. doi: 10.1016/j.ijplas.2007.07.016 – volume: 325 start-page: 1363 year: 2007 ident: 409_CR40 publication-title: J. Math. Anal. Appl. doi: 10.1016/j.jmaa.2006.02.071 – volume: 42 start-page: 1115 year: 1995 ident: 409_CR9 publication-title: J. ACM doi: 10.1145/227683.227684 – volume: 11 start-page: 796 year: 2001 ident: 409_CR18 publication-title: SIAM J. Optim. doi: 10.1137/S1052623400366802 – volume: 11&12 start-page: 625 year: 1999 ident: 409_CR45 publication-title: Optim. Methods Softw. doi: 10.1080/10556789908805766 – volume: 152 start-page: 1 year: 2008 ident: 409_CR17 publication-title: J. Appr. Theory doi: 10.1016/j.jat.2007.08.005 – ident: 409_CR34 doi: 10.1007/11751595_95
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Snippet	In this paper, we consider approximation algorithms for optimizing a generic multi-variate homogeneous polynomial function, subject to homogeneous quadratic... Issue Title: 20th International Symposium on Mathematical Programming - ISMP 2009 In this paper, we consider approximation algorithms for optimizing a generic...
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SubjectTerms	Algorithms Applied sciences Approximation Calculus of Variations and Optimal Control; Optimization Combinatorics Ellipsoids Exact sciences and technology Full Length Paper Intersections Linear algebra Magnetic resonance imaging Mathematical analysis Mathematical and Computational Physics Mathematical Methods in Physics Mathematical models Mathematical programming Mathematics Mathematics and Statistics Mathematics of Computing Maximization Numerical Analysis Operational research and scientific management Operational research. Management science Optimization Polynomials Quantum physics Signal processing Studies Theoretical Voice recognition
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Title	Approximation algorithms for homogeneous polynomial optimization with quadratic constraints
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