Strong duality in minimizing a quadratic form subject to two homogeneous quadratic inequalities over the unit sphere
In this paper, we study the strong duality for an optimization problem to minimize a homogeneous quadratic function subject to two homogeneous quadratic constraints over the unit sphere, called Problem (P) in this paper. When a feasible (P) fails to have a Slater point, we show that (P) always adopt...
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| Vydané v: | Journal of global optimization Ročník 76; číslo 1; s. 121 - 135 |
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| Hlavní autori: | , , |
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| Jazyk: | English |
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01.01.2020
Springer Springer Nature B.V |
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| ISSN: | 0925-5001, 1573-2916 |
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| Abstract | In this paper, we study the strong duality for an optimization problem to minimize a homogeneous quadratic function subject to two homogeneous quadratic constraints over the unit sphere, called Problem (P) in this paper. When a feasible (P) fails to have a Slater point, we show that (P) always adopts the strong duality. When (P) has a Slater point, we propose a set of conditions, called “
Property J
”, on an SDP relaxation of (P) and its conical dual. We show that (P) has the strong duality if and only if there exists at least one optimal solution to the SDP relaxation of (P) which
fails
Property J. Our techniques are based on various extensions of S-lemma as well as the matrix rank-one decomposition procedure introduced by Ai and Zhang. Many nontrivial examples are constructed to help understand the mechanism. |
|---|---|
| AbstractList | In this paper, we study the strong duality for an optimization problem to minimize a homogeneous quadratic function subject to two homogeneous quadratic constraints over the unit sphere, called Problem (P) in this paper. When a feasible (P) fails to have a Slater point, we show that (P) always adopts the strong duality. When (P) has a Slater point, we propose a set of conditions, called "Property J", on an SDP relaxation of (P) and its conical dual. We show that (P) has the strong duality if and only if there exists at least one optimal solution to the SDP relaxation of (P) which fails Property J. Our techniques are based on various extensions of S-lemma as well as the matrix rank-one decomposition procedure introduced by Ai and Zhang. Many nontrivial examples are constructed to help understand the mechanism. In this paper, we study the strong duality for an optimization problem to minimize a homogeneous quadratic function subject to two homogeneous quadratic constraints over the unit sphere, called Problem (P) in this paper. When a feasible (P) fails to have a Slater point, we show that (P) always adopts the strong duality. When (P) has a Slater point, we propose a set of conditions, called “ Property J ”, on an SDP relaxation of (P) and its conical dual. We show that (P) has the strong duality if and only if there exists at least one optimal solution to the SDP relaxation of (P) which fails Property J. Our techniques are based on various extensions of S-lemma as well as the matrix rank-one decomposition procedure introduced by Ai and Zhang. Many nontrivial examples are constructed to help understand the mechanism. |
| Audience | Academic |
| Author | Sheu, Ruey-Lin Nguyen, Van-Bong Nguyen, Thi Ngan |
| Author_xml | – sequence: 1 givenname: Van-Bong orcidid: 0000-0001-9046-8448 surname: Nguyen fullname: Nguyen, Van-Bong email: nvbong@ttn.edu.vn organization: Department of Mathematics, Tay Nguyen University – sequence: 2 givenname: Thi Ngan surname: Nguyen fullname: Nguyen, Thi Ngan organization: Department of Mathematics, Tay Nguyen University – sequence: 3 givenname: Ruey-Lin surname: Sheu fullname: Sheu, Ruey-Lin organization: Department of Mathematics, National Cheng Kung University |
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| Cites_doi | 10.1007/s10107-013-0716-2 10.1080/10556789308805542 10.1007/978-0-387-74759-0_540 10.1007/s10957-013-0417-2 10.1023/A:1021798932766 10.1137/07070601X 10.1137/1.9780898719857 10.1287/moor.2017.0879 10.1137/0904038 10.1016/j.laa.2018.10.011 10.1137/S1052623497322735 10.1017/S0962492900002518 10.1007/s10898-015-0315-2 10.1137/S003614450444614X 10.1090/S0002-9939-1961-0122827-1 10.1287/moor.28.2.246.14485 10.1137/1038003 10.1007/978-0-387-74759-0_538 10.1007/s10107-015-0893-2 10.1016/j.orl.2014.12.002 10.1137/15100624X 10.1007/s10589-013-9635-7 10.1287/moor.1030.0069 |
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| References | Vanderberghe, Boyd (CR29) 1995; 38 Ai, Zhang (CR1) 2009; 19 Bazarra, Sherali, Shetty (CR3) 1993 Fallahi, Salahi (CR9) 2014; 162 Hsia, Lin, Sheu (CR14) 2014; 10 Wolkowicz, Saigal, Vandenberghe (CR30) 2000 De Angelis, Toraldo, Floudas, Pardalos (CR8) 2009 Ferreira, Nemeth, Xiao (CR11) 2019; 562 Brickman (CR5) 1961; 12 Nguyen, Sheu, Xia (CR19) 2016; 64 Polyak (CR23) 1998; 99 Locatelli (CR16) 2015; 43 Moré (CR17) 1993; 2 Pitsoulis, Floudas, Pardalos (CR21) 2009 Pólik, Terlaky (CR22) 2007; 49 Solodov (CR27) 2004; 29 Boggs, Tolle (CR4) 1995; 4 Hao (CR13) 1982; 26 Yuan (CR33) 2015; 151 Ye, Floudas, Pardalos (CR32) 1992 Rendl, Wolkowicz (CR25) 1997; 77 Ferreira, Nemeth, Xiao (CR10) 2019; 562 Andreani, Martinez, Ramos, Silva (CR2) 2018; 43 Pardalos, Resende (CR20) 2002 Celis, Dennis, Tapia, Boggs, Byrd, Schnabel (CR6) 1984 Sturm, Zhang (CR28) 2003; 28 Moré, Sorensen (CR18) 1983; 4 Sakaue, Nakatsukasa, Takeda, Iwata (CR26) 2016; 26 Gould, Lucidi, Roma, Toint (CR12) 1999; 9 Conn, Gould, Toint (CR7) 2000 Yakubovich (CR31) 1977; 4 Pong, Wolkowicz (CR24) 2014; 58 Jeyakumar, Li (CR15) 2014; 147 L Pitsoulis (835_CR21) 2009 TK Pong (835_CR24) 2014; 58 PL De Angelis (835_CR8) 2009 VB Nguyen (835_CR19) 2016; 64 W Ai (835_CR1) 2009; 19 (835_CR30) 2000 OP Ferreira (835_CR10) 2019; 562 NIM Gould (835_CR12) 1999; 9 L Vanderberghe (835_CR29) 1995; 38 M Locatelli (835_CR16) 2015; 43 (835_CR20) 2002 OP Ferreira (835_CR11) 2019; 562 Y Ye (835_CR32) 1992 L Brickman (835_CR5) 1961; 12 MS Bazarra (835_CR3) 1993 JJ Moré (835_CR18) 1983; 4 MR Celis (835_CR6) 1984 PH Hao (835_CR13) 1982; 26 MV Solodov (835_CR27) 2004; 29 BT Polyak (835_CR23) 1998; 99 JF Sturm (835_CR28) 2003; 28 AR Conn (835_CR7) 2000 VA Yakubovich (835_CR31) 1977; 4 S Sakaue (835_CR26) 2016; 26 S Fallahi (835_CR9) 2014; 162 Y Yuan (835_CR33) 2015; 151 PT Boggs (835_CR4) 1995; 4 F Rendl (835_CR25) 1997; 77 R Andreani (835_CR2) 2018; 43 Y Hsia (835_CR14) 2014; 10 V Jeyakumar (835_CR15) 2014; 147 JJ Moré (835_CR17) 1993; 2 I Pólik (835_CR22) 2007; 49 |
| References_xml | – volume: 147 start-page: 171 issue: 1–2 year: 2014 end-page: 206 ident: CR15 article-title: Trust-region problems with linear inequality constraints: exact SDP relaxation, global optimality and robust optimization publication-title: Math. Program. doi: 10.1007/s10107-013-0716-2 – volume: 2 start-page: 189 year: 1993 end-page: 209 ident: CR17 article-title: Generalization of the trust region problem publication-title: Optim. Methods Softw. doi: 10.1080/10556789308805542 – start-page: 3170 year: 2009 end-page: 3171 ident: CR21 article-title: Quadratic programming with bound constraints publication-title: Encyclopedia of Optimization doi: 10.1007/978-0-387-74759-0_540 – volume: 162 start-page: 249 year: 2014 end-page: 256 ident: CR9 article-title: On the indefinite quadratic fractional optimization with two quadratic constraints publication-title: J. Optim. Theory Appl. doi: 10.1007/s10957-013-0417-2 – year: 2000 ident: CR30 publication-title: Handbook on Semidefinite Programming: Theory, Algorithms, and Applications – volume: 77 start-page: 273 issue: 2, Ser. B year: 1997 end-page: 299 ident: CR25 article-title: A semidefinite framework for trust region subproblems with applications to large scale minimization publication-title: Math. Program. – volume: 99 start-page: 553 year: 1998 end-page: 583 ident: CR23 article-title: Convexity of quadratic transformations and its use in control and optimization publication-title: J. Optim. Theory Appl. doi: 10.1023/A:1021798932766 – volume: 19 start-page: 1735 issue: 4 year: 2009 end-page: 1756 ident: CR1 article-title: Strong duality for the CDT subproblem: a necessary and sufficient condition publication-title: SIAM J. Optim. doi: 10.1137/07070601X – year: 2000 ident: CR7 publication-title: Trust-Region Methods doi: 10.1137/1.9780898719857 – volume: 43 start-page: 693 issue: 3 year: 2018 end-page: 717 ident: CR2 article-title: Strict constraint qualifications and sequential optimality conditions for constrained optimization publication-title: Math. Oper. Res. doi: 10.1287/moor.2017.0879 – volume: 4 start-page: 553 issue: 3 year: 1983 end-page: 572 ident: CR18 article-title: Computing a trust region step publication-title: SIAM J. Sci. Stat. Comput. doi: 10.1137/0904038 – volume: 562 start-page: 205 year: 2019 end-page: 222 ident: CR10 article-title: On the spherical quasi-convexity of quadratic functions publication-title: Linear Algebra Its Appl. doi: 10.1016/j.laa.2018.10.011 – start-page: 71 year: 1984 end-page: 82 ident: CR6 article-title: A trust region algorithm for nonlinear equality constrained optimization publication-title: Numerical Optimization – volume: 9 start-page: 504 issue: 2 year: 1999 end-page: 525 ident: CR12 article-title: Solving the trust-region subproblem using the Lanczos method publication-title: SIAM J. Optim. doi: 10.1137/S1052623497322735 – volume: 4 start-page: 1 year: 1995 end-page: 51 ident: CR4 article-title: Sequential quadratic programming publication-title: Acta Numer. doi: 10.1017/S0962492900002518 – year: 2002 ident: CR20 publication-title: Handbook of Applied Optimization – volume: 26 start-page: 105 year: 1982 end-page: 119 ident: CR13 article-title: Quadratically Constrained quadratic programming: some applications and a method for solution publication-title: Z. Oper. Res. – volume: 64 start-page: 399 year: 2016 end-page: 416 ident: CR19 article-title: Maximizing the sum of a generalized Rayleigh quotient and another Rayleigh quotient on the unit sphere via semidefinite programming publication-title: J. Glob. Optim. doi: 10.1007/s10898-015-0315-2 – volume: 49 start-page: 371 issue: 3 year: 2007 end-page: 418 ident: CR22 article-title: A survey of the S-lemma publication-title: SIAM Rev. doi: 10.1137/S003614450444614X – volume: 4 start-page: 73 year: 1977 end-page: 93 ident: CR31 article-title: S-procedure in nonlinear control theory publication-title: Vestnik Leningr. Univ. – volume: 12 start-page: 61 year: 1961 end-page: 66 ident: CR5 article-title: On the field of values of a matrix publication-title: Proc. Am. Math. Soc. doi: 10.1090/S0002-9939-1961-0122827-1 – volume: 562 start-page: 205 year: 2019 end-page: 222 ident: CR11 article-title: On the spherical quasi-convexity of quadratic functions publication-title: Linear Algebra Appl. doi: 10.1016/j.laa.2018.10.011 – volume: 28 start-page: 246 year: 2003 end-page: 267 ident: CR28 article-title: On cones of nonnegative quadratic functions publication-title: Math. Oper. Res. doi: 10.1287/moor.28.2.246.14485 – year: 1993 ident: CR3 publication-title: Nonlinear Programming Theory and Algorithms – volume: 38 start-page: 49 year: 1995 end-page: 95 ident: CR29 article-title: Semidefinite programming publication-title: SIAM Rev. doi: 10.1137/1038003 – start-page: 3161 year: 2009 end-page: 3166 ident: CR8 article-title: Quadratic programming with bound constraints publication-title: Encyclopedia of Optimization doi: 10.1007/978-0-387-74759-0_538 – year: 1992 ident: CR32 article-title: A new complexity result on minimization of a quadratic function with a sphere constraint publication-title: Recent Advances in Global Optimization – volume: 151 start-page: 249 issue: 1 year: 2015 end-page: 281 ident: CR33 article-title: Recent advances in trust region algorithms publication-title: Math. Program. doi: 10.1007/s10107-015-0893-2 – volume: 43 start-page: 126 issue: 2 year: 2015 end-page: 131 ident: CR16 article-title: Some results for quadratic problems with one or two quadratic constraints publication-title: Oper. Res. Lett. doi: 10.1016/j.orl.2014.12.002 – volume: 26 start-page: 1669 issue: 3 year: 2016 end-page: 1694 ident: CR26 article-title: Solving generalized CDT problems via two-parameter eigenvalues publication-title: SIAM J. Optim. doi: 10.1137/15100624X – volume: 58 start-page: 273 year: 2014 end-page: 322 ident: CR24 article-title: The generalized trust region subproblem publication-title: Comput. Optim. Appl. doi: 10.1007/s10589-013-9635-7 – volume: 10 start-page: 461 issue: 3 year: 2014 end-page: 481 ident: CR14 article-title: A revisit to quadratic programming with one inequality quadratic constraint via matrix pencil publication-title: Pac. J. Optim. – volume: 29 start-page: 64 issue: 1 year: 2004 end-page: 79 ident: CR27 article-title: On the sequential quadratically constrained quadratic programming methods publication-title: Math. Oper. Res. doi: 10.1287/moor.1030.0069 – volume-title: Handbook on Semidefinite Programming: Theory, Algorithms, and Applications year: 2000 ident: 835_CR30 – volume: 43 start-page: 693 issue: 3 year: 2018 ident: 835_CR2 publication-title: Math. Oper. Res. doi: 10.1287/moor.2017.0879 – volume: 64 start-page: 399 year: 2016 ident: 835_CR19 publication-title: J. Glob. Optim. doi: 10.1007/s10898-015-0315-2 – volume: 162 start-page: 249 year: 2014 ident: 835_CR9 publication-title: J. Optim. Theory Appl. doi: 10.1007/s10957-013-0417-2 – volume: 19 start-page: 1735 issue: 4 year: 2009 ident: 835_CR1 publication-title: SIAM J. Optim. doi: 10.1137/07070601X – volume: 562 start-page: 205 year: 2019 ident: 835_CR10 publication-title: Linear Algebra Its Appl. doi: 10.1016/j.laa.2018.10.011 – volume: 147 start-page: 171 issue: 1–2 year: 2014 ident: 835_CR15 publication-title: Math. Program. doi: 10.1007/s10107-013-0716-2 – volume: 10 start-page: 461 issue: 3 year: 2014 ident: 835_CR14 publication-title: Pac. J. Optim. – volume: 2 start-page: 189 year: 1993 ident: 835_CR17 publication-title: Optim. Methods Softw. doi: 10.1080/10556789308805542 – volume-title: Nonlinear Programming Theory and Algorithms year: 1993 ident: 835_CR3 – volume: 4 start-page: 73 year: 1977 ident: 835_CR31 publication-title: Vestnik Leningr. Univ. – volume: 562 start-page: 205 year: 2019 ident: 835_CR11 publication-title: Linear Algebra Appl. doi: 10.1016/j.laa.2018.10.011 – volume: 43 start-page: 126 issue: 2 year: 2015 ident: 835_CR16 publication-title: Oper. Res. Lett. doi: 10.1016/j.orl.2014.12.002 – start-page: 3161 volume-title: Encyclopedia of Optimization year: 2009 ident: 835_CR8 doi: 10.1007/978-0-387-74759-0_538 – volume: 26 start-page: 105 year: 1982 ident: 835_CR13 publication-title: Z. Oper. Res. – volume-title: Recent Advances in Global Optimization year: 1992 ident: 835_CR32 – volume: 4 start-page: 553 issue: 3 year: 1983 ident: 835_CR18 publication-title: SIAM J. Sci. Stat. Comput. doi: 10.1137/0904038 – volume: 9 start-page: 504 issue: 2 year: 1999 ident: 835_CR12 publication-title: SIAM J. Optim. doi: 10.1137/S1052623497322735 – volume: 49 start-page: 371 issue: 3 year: 2007 ident: 835_CR22 publication-title: SIAM Rev. doi: 10.1137/S003614450444614X – volume: 99 start-page: 553 year: 1998 ident: 835_CR23 publication-title: J. Optim. Theory Appl. doi: 10.1023/A:1021798932766 – start-page: 3170 volume-title: Encyclopedia of Optimization year: 2009 ident: 835_CR21 doi: 10.1007/978-0-387-74759-0_540 – volume-title: Handbook of Applied Optimization year: 2002 ident: 835_CR20 – volume: 151 start-page: 249 issue: 1 year: 2015 ident: 835_CR33 publication-title: Math. Program. doi: 10.1007/s10107-015-0893-2 – volume-title: Trust-Region Methods year: 2000 ident: 835_CR7 doi: 10.1137/1.9780898719857 – volume: 29 start-page: 64 issue: 1 year: 2004 ident: 835_CR27 publication-title: Math. Oper. Res. doi: 10.1287/moor.1030.0069 – volume: 12 start-page: 61 year: 1961 ident: 835_CR5 publication-title: Proc. Am. Math. Soc. doi: 10.1090/S0002-9939-1961-0122827-1 – volume: 58 start-page: 273 year: 2014 ident: 835_CR24 publication-title: Comput. Optim. Appl. doi: 10.1007/s10589-013-9635-7 – volume: 4 start-page: 1 year: 1995 ident: 835_CR4 publication-title: Acta Numer. doi: 10.1017/S0962492900002518 – start-page: 71 volume-title: Numerical Optimization year: 1984 ident: 835_CR6 – volume: 77 start-page: 273 issue: 2, Ser. B year: 1997 ident: 835_CR25 publication-title: Math. Program. – volume: 26 start-page: 1669 issue: 3 year: 2016 ident: 835_CR26 publication-title: SIAM J. Optim. doi: 10.1137/15100624X – volume: 38 start-page: 49 year: 1995 ident: 835_CR29 publication-title: SIAM Rev. doi: 10.1137/1038003 – volume: 28 start-page: 246 year: 2003 ident: 835_CR28 publication-title: Math. Oper. Res. doi: 10.1287/moor.28.2.246.14485 |
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| SubjectTerms | Computer Science Mathematics Mathematics and Statistics Operations Research/Decision Theory Optimization Quadratic equations Quadratic forms Real Functions |
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| Title | Strong duality in minimizing a quadratic form subject to two homogeneous quadratic inequalities over the unit sphere |
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