Difference of convex functions optimization algorithms (DCA) for globally minimizing nonconvex quadratic forms on Euclidean balls and spheres

We present DCA for globally minimizing quadratic forms on Euclidean balls and spheres. Since these problems admit at most one local-nonglobal minimizer, DCA converges in general to a solution for these problems. Numerical simulations show robustness, stability and efficiency of DCA with respect to r...

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Published in:	Operations research letters Vol. 19; no. 5; pp. 207 - 216
Main Authors:	Tao, Pham Dinh, An, Le Thi Hoai
Format:	Journal Article
Language:	English
Published:	Amsterdam Elsevier B.V 01.11.1996 Elsevier
Subjects:	Applied sciences Computer Science d.c. optimization d.c. optimization algorithms Exact sciences and technology Local and global optimality conditions Mathematical programming Nonconvex quadratic minimization Operational research and scientific management Operational research. Management science Optimization. Search problems d.c. optimization algorithms Local and global optimality conditions Nonconvex quadratic minimization d.c. optimization Non convex programming Algorithms Euclidean theory Optimality condition Spheres Quadratic programming Optimization
ISSN:	0167-6377, 1872-7468
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Abstract	We present DCA for globally minimizing quadratic forms on Euclidean balls and spheres. Since these problems admit at most one local-nonglobal minimizer, DCA converges in general to a solution for these problems. Numerical simulations show robustness, stability and efficiency of DCA with respect to related standard methods.
AbstractList	We present DCA for globally minimizing quadratic forms on Euclidean balls and spheres. Since these problems admit at most one local-nonglobal minimizer, DCA converges in general to a solution for these problems. Numerical simulations show robustness, stability and efficiency of DCA with respect to related standard methods.
Author	An, Le Thi Hoai Tao, Pham Dinh
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Keywords	d.c. optimization algorithms Local and global optimality conditions Nonconvex quadratic minimization d.c. optimization Non convex programming Algorithms Euclidean theory Optimality condition Spheres Quadratic programming Optimization
Language	English
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References	Tao (BIB15) 1981 Rockafellar (BIB26) 1976; 14 Gander, Golub, Von Matt (BIB6) 1989; 114/115 Bental, Teboulle (BIB2) 1993 More (BIB12) 1983 Tao, An (BIB19) 1994 Mahey, Tao (BIB10) 1995; 5 Tao, Wang (BIB24) 1990; 24 Golub, Von Matt (BIB8) 1991; 59 Tao (BIB22) 1989 Tao (BIB16) 1984; 62 Tao, El Bernoussi (BIB23) 1988; Vol. 84 Sorensen (BIB27) 1982; 19 Polyak (BIB14) 1987 Gay (BIB7) 1981; 2 An (BIB1) 1994 Tao (BIB18) 1986 Tao (BIB17) 1985; 45 Tao, An (BIB20) 1994; 318 Mahey, Tao (BIB9) 1993; 27 Toland (BIB29) 1979; 60 Martinez (BIB11) 1994; 4 Tao, An (BIB21) 1995; 2 Rockafellar (BIB25) 1970 Fletcher (BIB4) 1991 Clermont, De La Lande, Tao (BIB3) 1991; 13 Flippo, Jansen (BIB5) 1993 More, Sorensen (BIB13) 1983; 4 Stern, Wolkowicz (BIB28) 1993; 5 Fletcher (10.1016/S0167-6377(96)00036-3_BIB4) 1991 Golub (10.1016/S0167-6377(96)00036-3_BIB8) 1991; 59 Tao (10.1016/S0167-6377(96)00036-3_BIB19) 1994 Tao (10.1016/S0167-6377(96)00036-3_BIB24) 1990; 24 Tao (10.1016/S0167-6377(96)00036-3_BIB15) 1981 Mahey (10.1016/S0167-6377(96)00036-3_BIB10) 1995; 5 Clermont (10.1016/S0167-6377(96)00036-3_BIB3) 1991; 13 Martinez (10.1016/S0167-6377(96)00036-3_BIB11) 1994; 4 Tao (10.1016/S0167-6377(96)00036-3_BIB18) 1986 More (10.1016/S0167-6377(96)00036-3_BIB12) 1983 Rockafellar (10.1016/S0167-6377(96)00036-3_BIB25) 1970 Mahey (10.1016/S0167-6377(96)00036-3_BIB9) 1993; 27 Tao (10.1016/S0167-6377(96)00036-3_BIB21) 1995; 2 Stern (10.1016/S0167-6377(96)00036-3_BIB28) 1993; 5 Gander (10.1016/S0167-6377(96)00036-3_BIB6) 1989; 114/115 Gay (10.1016/S0167-6377(96)00036-3_BIB7) 1981; 2 Sorensen (10.1016/S0167-6377(96)00036-3_BIB27) 1982; 19 Tao (10.1016/S0167-6377(96)00036-3_BIB16) 1984; 62 An (10.1016/S0167-6377(96)00036-3_BIB1) 1994 Tao (10.1016/S0167-6377(96)00036-3_BIB20) 1994; 318 Polyak (10.1016/S0167-6377(96)00036-3_BIB14) 1987 Bental (10.1016/S0167-6377(96)00036-3_BIB2) 1993 Tao (10.1016/S0167-6377(96)00036-3_BIB22) 1989 More (10.1016/S0167-6377(96)00036-3_BIB13) 1983; 4 Flippo (10.1016/S0167-6377(96)00036-3_BIB5) 1993 Tao (10.1016/S0167-6377(96)00036-3_BIB17) 1985; 45 Tao (10.1016/S0167-6377(96)00036-3_BIB23) 1988; Vol. 84 Toland (10.1016/S0167-6377(96)00036-3_BIB29) 1979; 60 Rockafellar (10.1016/S0167-6377(96)00036-3_BIB26) 1976; 14
References_xml	– year: 1994 ident: BIB1 article-title: Analyse numérique des algorithmes de l'Optimisation d.c. Approches locales et globales. Code et simulations numériques en grande dimension Applications publication-title: Thèse de Doctorat de l'Université de Rouen – volume: 45 start-page: 377 year: 1985 end-page: 440 ident: BIB17 article-title: Algorithmes de calcul du maximum d'une forme quadratique sur la boule unité de la norme du maximum publication-title: Numer. Math. – volume: 318 year: 1994 ident: BIB20 article-title: Stabilite de la dualité lagrangienne en optimisation d.c. (difference de deux fonctions convexes) publication-title: C.R. Acad. Sci. Paris – volume: 13 start-page: 339 year: 1991 end-page: 371 ident: BIB3 article-title: Analysis of plane and axisymmetric flows of incompressible fluids with the stream tube method: Numerical simulation by Trust region algorithm publication-title: Internat. J. Numer. Methods Fluids – volume: 60 start-page: 177 year: 1979 end-page: 183 ident: BIB29 article-title: On subdifferential calculus and duality in nonconvex optimization publication-title: Bull. Soc. Math. France – volume: 59 start-page: 561 year: 1991 end-page: 580 ident: BIB8 article-title: Quadratically constrained least squares and quadratic problems publication-title: Numer. Math. – volume: 114/115 start-page: 815 year: 1989 end-page: 839 ident: BIB6 article-title: A constrained eigenvalue problem publication-title: Linear Algebra Appl. – volume: 2 start-page: 186 year: 1981 end-page: 197 ident: BIB7 article-title: Computing optimal locally constrained steps publication-title: SIAM J. Sci. Statist. Comput. – volume: Vol. 84 start-page: 276 year: 1988 end-page: 294 ident: BIB23 article-title: Duality in d.c. (difference of convex functions) optimization. Subgradient methods publication-title: International Series of Numer Math. – year: 1993 ident: BIB5 article-title: Duality and sensitivity in nonconvex quadratic optimization over a ellipsoid publication-title: Technical Report – start-page: 258 year: 1983 end-page: 287 ident: BIB12 article-title: Recent developments in algorithm and software for trust region methods publication-title: Mathematical Programming, The State of the Art – volume: 4 start-page: 553 year: 1983 end-page: 572 ident: BIB13 article-title: Computing a trust region step publication-title: SIAM J. Sci. Statist. Comput. – volume: 4 start-page: 159 year: 1994 end-page: 176 ident: BIB11 article-title: Local minimizers of quadratic functions on euclidean balls and spheres publication-title: SIAM J. Optim. – volume: 62 start-page: 163 year: 1984 end-page: 182 ident: BIB16 article-title: Convergence of subgradient method for computing the bound norm of matrices publication-title: Linear Algebra Appl. – volume: 5 start-page: 286 year: 1993 end-page: 313 ident: BIB28 article-title: Indefinite trust region subproblems and nonsymmetric eigenvalue perturbations publication-title: SIAM J. Optim. – year: 1991 ident: BIB4 article-title: Practical Methods of Optimization – year: 1989 ident: BIB22 article-title: Méthodes numeriques pour la minimisation globale d'une forme quadratique (convexe ou non convexe) sur une boule et une sphère euclidiennes publication-title: Rapport de Recherche, Université – year: 1987 ident: BIB14 article-title: Introduction to Optimization. Optimization Software – volume: 24 start-page: 523 year: 1990 end-page: 553 ident: BIB24 article-title: Training multi-layered neural network with a Trust region based algorithm publication-title: Math. Modell. Numer. Anal. – year: 1970 ident: BIB25 article-title: Convex Analysis – year: 1986 ident: BIB18 article-title: Algorithms for solving a class of non-convex optimization problems, Methods of subgradients publication-title: Fermat Days 85, Mathematics for Optimization – year: 1994 ident: BIB19 article-title: Optimisation d.c. (difference de deux fonctions convexes). Dualite and stability. Optimalités locale and globale. Algorithmes de l'optimisation d.c. (DCA) publication-title: L.M.I., CNRS URA 1378 – year: 1981 ident: BIB15 article-title: Contribution à la théorie de normes and ses applications à l'analyse numérique publication-title: Thèse de Doctorat d'Etat Es Science – volume: 27 start-page: 375 year: 1993 end-page: 395 ident: BIB9 article-title: Partial regularization of the sum of two maximal monotone operators publication-title: Math. Modell. Numer. Anal. – volume: 14 start-page: 877 year: 1976 end-page: 898 ident: BIB26 article-title: Monotone operators and the proximal point algorithm in convex programming publication-title: SIAM J. Control Optim. – volume: 19 start-page: 409 year: 1982 end-page: 426 ident: BIB27 article-title: Newton's method with a model trust region modification publication-title: SIAM J. Numer. Anal. – year: 1993 ident: BIB2 article-title: Hidden convexity in some nonconvex quadratically constrained quadratic programming publication-title: Technical report – volume: 2 start-page: 263 year: 1995 end-page: 276 ident: BIB21 article-title: Lagrangian stability and global optimality on nonconvex quadratic minimization over Euclidean balls and spheres publication-title: J. Convex Anal. – volume: 5 start-page: 454 year: 1995 end-page: 468 ident: BIB10 article-title: Proximal decomposition of the graph of maximal monotone operator publication-title: SIAM J. Optim. – volume: 27 start-page: 375 year: 1993 ident: 10.1016/S0167-6377(96)00036-3_BIB9 article-title: Partial regularization of the sum of two maximal monotone operators publication-title: Math. Modell. Numer. Anal. doi: 10.1051/m2an/1993270303751 – year: 1994 ident: 10.1016/S0167-6377(96)00036-3_BIB1 article-title: Analyse numérique des algorithmes de l'Optimisation d.c. Approches locales et globales. Code et simulations numériques en grande dimension Applications – volume: 19 start-page: 409 year: 1982 ident: 10.1016/S0167-6377(96)00036-3_BIB27 article-title: Newton's method with a model trust region modification publication-title: SIAM J. Numer. Anal. doi: 10.1137/0719026 – volume: 45 start-page: 377 year: 1985 ident: 10.1016/S0167-6377(96)00036-3_BIB17 article-title: Algorithmes de calcul du maximum d'une forme quadratique sur la boule unité de la norme du maximum publication-title: Numer. Math. doi: 10.1007/BF01391415 – volume: Vol. 84 start-page: 276 year: 1988 ident: 10.1016/S0167-6377(96)00036-3_BIB23 article-title: Duality in d.c. (difference of convex functions) optimization. Subgradient methods – year: 1994 ident: 10.1016/S0167-6377(96)00036-3_BIB19 article-title: Optimisation d.c. (difference de deux fonctions convexes). Dualite and stability. Optimalités locale and globale. Algorithmes de l'optimisation d.c. (DCA) – volume: 318 year: 1994 ident: 10.1016/S0167-6377(96)00036-3_BIB20 article-title: Stabilite de la dualité lagrangienne en optimisation d.c. (difference de deux fonctions convexes) publication-title: C.R. Acad. Sci. Paris – year: 1989 ident: 10.1016/S0167-6377(96)00036-3_BIB22 article-title: Méthodes numeriques pour la minimisation globale d'une forme quadratique (convexe ou non convexe) sur une boule et une sphère euclidiennes – year: 1993 ident: 10.1016/S0167-6377(96)00036-3_BIB5 article-title: Duality and sensitivity in nonconvex quadratic optimization over a ellipsoid – volume: 114/115 start-page: 815 year: 1989 ident: 10.1016/S0167-6377(96)00036-3_BIB6 article-title: A constrained eigenvalue problem publication-title: Linear Algebra Appl. doi: 10.1016/0024-3795(89)90494-1 – volume: 14 start-page: 877 year: 1976 ident: 10.1016/S0167-6377(96)00036-3_BIB26 article-title: Monotone operators and the proximal point algorithm in convex programming publication-title: SIAM J. Control Optim. doi: 10.1137/0314056 – volume: 2 start-page: 186 year: 1981 ident: 10.1016/S0167-6377(96)00036-3_BIB7 article-title: Computing optimal locally constrained steps publication-title: SIAM J. Sci. Statist. Comput. doi: 10.1137/0902016 – volume: 2 start-page: 263 year: 1995 ident: 10.1016/S0167-6377(96)00036-3_BIB21 article-title: Lagrangian stability and global optimality on nonconvex quadratic minimization over Euclidean balls and spheres publication-title: J. Convex Anal. – start-page: 258 year: 1983 ident: 10.1016/S0167-6377(96)00036-3_BIB12 article-title: Recent developments in algorithm and software for trust region methods – volume: 62 start-page: 163 year: 1984 ident: 10.1016/S0167-6377(96)00036-3_BIB16 article-title: Convergence of subgradient method for computing the bound norm of matrices publication-title: Linear Algebra Appl. doi: 10.1016/0024-3795(84)90093-4 – year: 1981 ident: 10.1016/S0167-6377(96)00036-3_BIB15 article-title: Contribution à la théorie de normes and ses applications à l'analyse numérique – year: 1991 ident: 10.1016/S0167-6377(96)00036-3_BIB4 – year: 1970 ident: 10.1016/S0167-6377(96)00036-3_BIB25 – volume: 5 start-page: 454 year: 1995 ident: 10.1016/S0167-6377(96)00036-3_BIB10 article-title: Proximal decomposition of the graph of maximal monotone operator publication-title: SIAM J. Optim. doi: 10.1137/0805023 – volume: 5 start-page: 286 year: 1993 ident: 10.1016/S0167-6377(96)00036-3_BIB28 article-title: Indefinite trust region subproblems and nonsymmetric eigenvalue perturbations publication-title: SIAM J. Optim. doi: 10.1137/0805016 – volume: 4 start-page: 159 year: 1994 ident: 10.1016/S0167-6377(96)00036-3_BIB11 article-title: Local minimizers of quadratic functions on euclidean balls and spheres publication-title: SIAM J. Optim. doi: 10.1137/0804009 – year: 1987 ident: 10.1016/S0167-6377(96)00036-3_BIB14 – volume: 4 start-page: 553 year: 1983 ident: 10.1016/S0167-6377(96)00036-3_BIB13 article-title: Computing a trust region step publication-title: SIAM J. Sci. Statist. Comput. doi: 10.1137/0904038 – year: 1993 ident: 10.1016/S0167-6377(96)00036-3_BIB2 article-title: Hidden convexity in some nonconvex quadratically constrained quadratic programming – volume: 59 start-page: 561 year: 1991 ident: 10.1016/S0167-6377(96)00036-3_BIB8 article-title: Quadratically constrained least squares and quadratic problems publication-title: Numer. Math. doi: 10.1007/BF01385796 – volume: 13 start-page: 339 year: 1991 ident: 10.1016/S0167-6377(96)00036-3_BIB3 article-title: Analysis of plane and axisymmetric flows of incompressible fluids with the stream tube method: Numerical simulation by Trust region algorithm publication-title: Internat. J. Numer. Methods Fluids doi: 10.1002/fld.1650130308 – volume: 60 start-page: 177 year: 1979 ident: 10.1016/S0167-6377(96)00036-3_BIB29 article-title: On subdifferential calculus and duality in nonconvex optimization publication-title: Bull. Soc. Math. France – year: 1986 ident: 10.1016/S0167-6377(96)00036-3_BIB18 article-title: Algorithms for solving a class of non-convex optimization problems, Methods of subgradients – volume: 24 start-page: 523 year: 1990 ident: 10.1016/S0167-6377(96)00036-3_BIB24 article-title: Training multi-layered neural network with a Trust region based algorithm publication-title: Math. Modell. Numer. Anal. doi: 10.1051/m2an/1990240405231
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Snippet	We present DCA for globally minimizing quadratic forms on Euclidean balls and spheres. Since these problems admit at most one local-nonglobal minimizer, DCA...
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SubjectTerms	Applied sciences Computer Science d.c. optimization d.c. optimization algorithms Exact sciences and technology Local and global optimality conditions Mathematical programming Nonconvex quadratic minimization Operational research and scientific management Operational research. Management science Optimization. Search problems
Title	Difference of convex functions optimization algorithms (DCA) for globally minimizing nonconvex quadratic forms on Euclidean balls and spheres
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