Interior Proximal Algorithm for Quasiconvex Programming Problems and Variational Inequalities with Linear Constraints
In this paper, we propose two interior proximal algorithms inspired by the logarithmic-quadratic proximal method. The first method we propose is for general linearly constrained quasiconvex minimization problems. For this method, we prove global convergence when the regularization parameters go to z...
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| Veröffentlicht in: | Journal of optimization theory and applications Jg. 154; H. 1; S. 217 - 234 |
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| Format: | Journal Article |
| Sprache: | Englisch |
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01.07.2012
Springer Nature B.V |
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| ISSN: | 0022-3239, 1573-2878 |
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| Abstract | In this paper, we propose two interior proximal algorithms inspired by the logarithmic-quadratic proximal method. The first method we propose is for general linearly constrained quasiconvex minimization problems. For this method, we prove global convergence when the regularization parameters go to zero. The latter assumption can be dropped when the function is assumed to be pseudoconvex. We also obtain convergence results for quasimonotone variational inequalities, which are more general than monotone ones. |
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| AbstractList | In this paper, we propose two interior proximal algorithms inspired by the logarithmic-quadratic proximal method. The first method we propose is for general linearly constrained quasiconvex minimization problems. For this method, we prove global convergence when the regularization parameters go to zero. The latter assumption can be dropped when the function is assumed to be pseudoconvex. We also obtain convergence results for quasimonotone variational inequalities, which are more general than monotone ones. In this paper, we propose two interior proximal algorithms inspired by the logarithmic-quadratic proximal method. The first method we propose is for general linearly constrained quasiconvex minimization problems. For this method, we prove global convergence when the regularization parameters go to zero. The latter assumption can be dropped when the function is assumed to be pseudoconvex. We also obtain convergence results for quasimonotone variational inequalities, which are more general than monotone ones.[PUBLICATION ABSTRACT] |
| Author | Brito, Arnaldo S. da Cruz Neto, J. X. Oliveira, P. Roberto Lopes, Jurandir O. |
| Author_xml | – sequence: 1 givenname: Arnaldo S. surname: Brito fullname: Brito, Arnaldo S. organization: Federal University of Rio de Janeiro – sequence: 2 givenname: J. X. surname: da Cruz Neto fullname: da Cruz Neto, J. X. organization: Federal University of Piaui – sequence: 3 givenname: Jurandir O. surname: Lopes fullname: Lopes, Jurandir O. email: jurandir@ufpi.br organization: Federal University of Piaui – sequence: 4 givenname: P. Roberto surname: Oliveira fullname: Oliveira, P. Roberto organization: COPPE/Sistemas-Universidade Federal do Rio de Janeiro |
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| CitedBy_id | crossref_primary_10_1007_s12190_024_02219_9 crossref_primary_10_1007_s10479_020_03622_8 crossref_primary_10_1186_s13660_018_1852_2 crossref_primary_10_1007_s11590_022_01874_w crossref_primary_10_1007_s10898_015_0367_3 crossref_primary_10_1007_s10589_020_00217_8 crossref_primary_10_1080_10556788_2025_2531481 crossref_primary_10_1007_s10589_014_9659_7 crossref_primary_10_1007_s11228_019_00517_0 crossref_primary_10_1016_j_ejor_2015_05_041 crossref_primary_10_1007_s10898_021_01110_2 crossref_primary_10_1080_02331934_2022_2112580 crossref_primary_10_1007_s10957_021_01996_8 crossref_primary_10_1007_s11075_021_01170_1 crossref_primary_10_1007_s10898_022_01226_z crossref_primary_10_1007_s10851_019_00916_w crossref_primary_10_1080_02331934_2023_2231002 |
| Cites_doi | 10.1023/A:1022693822102 10.1287/moor.19.4.790 10.1007/s10898-006-9013-4 10.1287/moor.1030.0062 10.1007/978-1-4613-3326-5 10.1137/S1052623495292130 10.1007/978-3-642-02431-3 10.1023/A:1012234817482 10.1023/A:1022618915698 10.1080/02331939908844423 10.1023/A:1008607511915 10.1016/j.ejor.2009.03.045 10.5802/aif.280 10.1007/BF01582255 10.1287/moor.24.3.645 10.1080/02331930902884273 10.1007/BF00932654 10.1023/A:1023905907248 10.1287/moor.17.3.670 10.1137/0803026 10.1137/0314056 10.1007/BF00940051 10.1007/978-1-4613-3341-8 |
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| DOI | 10.1007/s10957-012-0002-0 |
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| Keywords | Quasiconvex function Quasiconvex linearly constrained problems Proximal algorithm Quasimonotone operator Variational inequalities |
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| References | Bajona-Xandrei, Martinez-Legaz (CR17) 1999; 45 El Farouq (CR31) 2001; 2 Teboulle (CR8) 1992; 17 Aussel (CR27) 1998; 97 Harker, Pang (CR32) 1990; 48 Karamardian (CR24) 1976; 18 Auslender, Teboulle, Ben-Tiba (CR4) 1999; 12 Souza, Oliveira, Cruz Neto, Soubeyaran (CR13) 2010; 2 Daniilidis, Hadjisavvas (CR29) 1999; 102 Mas-Colell, Whinston, Green (CR15) 1995 Rockafellar (CR2) 1976; 14 Chen, Teboulle (CR6) 1993; 3 Iusem, Svaiter, Teboulle (CR7) 1994; 19 Chen, Pan (CR10) 2008; 4 Cunha, Neto Cruz, Oliveira (CR11) 2010; 5 Teboulle (CR9) 1997; 7 Papa, Oliveira (CR12) 2009; 355 Auslender, Teboulle, Ben-Tiba (CR3) 1999; 24 Facchine, Pang (CR33) 2003 Abdellah (CR18) 2006; 36 Bnouhachem (CR22) 2006; 36 Auslender, Teboulle (CR21) 2004; 29 Martinet (CR1) 1970; 4 Brezis (CR25) 1968; 18 Penot (CR20) 2003; 3 Aussel, Corvellec, Lassonde (CR28) 1994; 1 Hadjisavvas (CR30) 2003; 10 Clarke (CR26) 1983 Bazaraa, Sherali, Shetty (CR19) 1993 Censor, Zenios (CR5) 1992; 73 Rockafellar, Wets (CR23) 1998 Gromicho (CR16) 1998 Crouzeix, Martinez-Legaz, Volle (CR14) 1998 F.H. Clarke (2_CR26) 1983 Y. Censor (2_CR5) 1992; 73 B. Martinet (2_CR1) 1970; 4 S. Karamardian (2_CR24) 1976; 18 J. Gromicho (2_CR16) 1998 M.S. Bazaraa (2_CR19) 1993 F. Facchine (2_CR33) 2003 R.T. Rockafellar (2_CR2) 1976; 14 G. Chen (2_CR6) 1993; 3 F.G.M. Cunha (2_CR11) 2010; 5 D. Aussel (2_CR28) 1994; 1 A. Auslender (2_CR3) 1999; 24 J.-S. Chen (2_CR10) 2008; 4 P.T. Harker (2_CR32) 1990; 48 M. Teboulle (2_CR8) 1992; 17 R.T. Rockafellar (2_CR23) 1998 A. Daniilidis (2_CR29) 1999; 102 Q.A. Papa (2_CR12) 2009; 355 N. Farouq El (2_CR31) 2001; 2 B. Abdellah (2_CR18) 2006; 36 D. Aussel (2_CR27) 1998; 97 N. Hadjisavvas (2_CR30) 2003; 10 A. Auslender (2_CR4) 1999; 12 A. Bnouhachem (2_CR22) 2006; 36 A.N. Iusem (2_CR7) 1994; 19 A. Auslender (2_CR21) 2004; 29 H. Brezis (2_CR25) 1968; 18 A. Mas-Colell (2_CR15) 1995 C. Bajona-Xandrei (2_CR17) 1999; 45 J.-P. Crouzeix (2_CR14) 1998 M. Teboulle (2_CR9) 1997; 7 S.S. Souza (2_CR13) 2010; 2 J.-P. Penot (2_CR20) 2003; 3 |
| References_xml | – volume: 102 start-page: 525 year: 1999 end-page: 536 ident: CR29 article-title: Characterization of nonsmooth semistrictly quasiconvex and strictly quasiconvex functions publication-title: J. Optim. Theory Appl. doi: 10.1023/A:1022693822102 – volume: 19 start-page: 790 year: 1994 end-page: 814 ident: CR7 article-title: Entropy-like proximal methods in convex programming publication-title: Math. Oper. Res. doi: 10.1287/moor.19.4.790 – volume: 36 start-page: 351 year: 2006 end-page: 363 ident: CR18 article-title: An LQP method for pseudomonotone variational inequalities publication-title: J. Glob. Optim. doi: 10.1007/s10898-006-9013-4 – volume: 29 start-page: 1 year: 2004 end-page: 26 ident: CR21 article-title: Interior gradient and epsilon-subgradient descent methods for constrained convex minimization publication-title: Math. Oper. Res. doi: 10.1287/moor.1030.0062 – year: 1983 ident: CR26 publication-title: Optimization and Nonsmooth Analysis – year: 1995 ident: CR15 publication-title: Microeconomic Theory – year: 1998 ident: CR16 publication-title: Quasiconvex Optimization and Location Theory doi: 10.1007/978-1-4613-3326-5 – volume: 10 start-page: 459 year: 2003 end-page: 469 ident: CR30 article-title: Continuity and maximality properties of pseudomonote operators publication-title: J. Convex Anal. – volume: 7 start-page: 1069 year: 1997 end-page: 1083 ident: CR9 article-title: Convergence of proximal-like algorithms publication-title: SIAM J. Optim. doi: 10.1137/S1052623495292130 – year: 1998 ident: CR23 publication-title: Variational Analysis doi: 10.1007/978-3-642-02431-3 – volume: 2 start-page: 305 year: 2001 end-page: 326 ident: CR31 article-title: Pseudomonotone variational inequalities: convergence of the auxiliar problem method publication-title: J. Optim. Theory Appl. doi: 10.1023/A:1012234817482 – volume: 97 start-page: 29 year: 1998 end-page: 45 ident: CR27 article-title: Subdifferential properties of quasiconvex and pseudoconvex functions: unified approach publication-title: J. Optim. Theory Appl. doi: 10.1023/A:1022618915698 – year: 1998 ident: CR14 publication-title: Generalized Convexity, Generalized Monotonicity. Non Convex Optimization and Its Applications – volume: 45 start-page: 1 year: 1999 end-page: 22 ident: CR17 article-title: Lower subdifferentiability in minimax fractional programming publication-title: Optimization doi: 10.1080/02331939908844423 – volume: 12 start-page: 31 year: 1999 end-page: 40 ident: CR4 article-title: A logarithmic-quadratic proximal method for variational inequalities publication-title: Comput. Optim. Appl. doi: 10.1023/A:1008607511915 – year: 1993 ident: CR19 publication-title: Nonlinear Programming: Theory and Algorithms – volume: 4 start-page: 154 year: 1970 end-page: 158 ident: CR1 article-title: Regularisation, d’inéquations variationnelles par approximations sucessives publication-title: Rev. Fr. Autom. Inform. Rech. Opér. – volume: 4 start-page: 319 year: 2008 end-page: 333 ident: CR10 article-title: A proximal-like algorithm for a class of nonconvex programming publication-title: Pac. J. Optim. – volume: 2 start-page: 365 year: 2010 end-page: 376 ident: CR13 article-title: A proximal method with separable distances Bregman for quasiconvex minimization over the nonnegative orthant publication-title: Eur. J. Oper. Res. doi: 10.1016/j.ejor.2009.03.045 – volume: 355 start-page: 469 year: 2009 end-page: 478 ident: CR12 article-title: Proximal point methods for quasiconvex and convex function with Bregman distances on Hadamard manifolds publication-title: J. Convex Anal. – volume: 18 start-page: 115 year: 1968 end-page: 175 ident: CR25 article-title: Equations et inequations nonlineaires dans les espaces vectoriels en dualité publication-title: Ann. Inst. Fourier doi: 10.5802/aif.280 – volume: 48 start-page: 161 year: 1990 end-page: 220 ident: CR32 article-title: Finite-dimensional variational inequality and nonlinear complementarity problems: a survey of theory, algorithms, and applications publication-title: Math. Program. doi: 10.1007/BF01582255 – volume: 24 start-page: 645 year: 1999 end-page: 668 ident: CR3 article-title: Interior proximal and multiplier methods based on second order homogeneous kernels publication-title: Math. Oper. Res. doi: 10.1287/moor.24.3.645 – volume: 5 start-page: 777 year: 2010 end-page: 792 ident: CR11 article-title: A proximal point algorithm with -divergence to quasiconvex programming publication-title: Optimization doi: 10.1080/02331930902884273 – volume: 18 start-page: 445 year: 1976 end-page: 455 ident: CR24 article-title: Complementarity problems over cones with monotone and pseudomonotone maps publication-title: J. Optim. Theory Appl. doi: 10.1007/BF00932654 – volume: 3 start-page: 627 year: 2003 end-page: 636 ident: CR20 article-title: Characterization of solution sets of quasiconvex programs publication-title: J. Optim. Theory Appl. doi: 10.1023/A:1023905907248 – volume: 36 start-page: 351 year: 2006 end-page: 363 ident: CR22 article-title: An LQP method for pseudomonotone variational inequalities publication-title: J. Glob. Optim. doi: 10.1007/s10898-006-9013-4 – volume: 17 start-page: 670 year: 1992 end-page: 690 ident: CR8 article-title: Entropic proximal mapping with applications to nonlinear programming publication-title: Math. Oper. Res. doi: 10.1287/moor.17.3.670 – year: 2003 ident: CR33 publication-title: Finite-Dimensional Variational Inequality and Complementarity Problems – volume: 3 start-page: 538 year: 1993 end-page: 543 ident: CR6 article-title: Convergence analysis of a proximal-like minimization algorithm using Bregman functions publication-title: SIAM J. Optim. doi: 10.1137/0803026 – volume: 14 start-page: 877 year: 1976 end-page: 898 ident: CR2 article-title: Monotone operators and the proximal point algorithm publication-title: SIAM J. Control Optim. doi: 10.1137/0314056 – volume: 1 start-page: 195 year: 1994 end-page: 201 ident: CR28 article-title: Subdifferential characterization of quasiconvexity and convexity publication-title: J. Convex Anal. – volume: 73 start-page: 451 year: 1992 end-page: 464 ident: CR5 article-title: The proximal minimization algorithm with D-functions publication-title: J. Optim. Theory Appl. doi: 10.1007/BF00940051 – volume-title: Generalized Convexity, Generalized Monotonicity. Non Convex Optimization and Its Applications year: 1998 ident: 2_CR14 doi: 10.1007/978-1-4613-3341-8 – volume: 3 start-page: 538 year: 1993 ident: 2_CR6 publication-title: SIAM J. Optim. doi: 10.1137/0803026 – volume: 36 start-page: 351 year: 2006 ident: 2_CR18 publication-title: J. Glob. Optim. doi: 10.1007/s10898-006-9013-4 – volume: 48 start-page: 161 year: 1990 ident: 2_CR32 publication-title: Math. Program. doi: 10.1007/BF01582255 – volume: 97 start-page: 29 year: 1998 ident: 2_CR27 publication-title: J. Optim. Theory Appl. doi: 10.1023/A:1022618915698 – volume: 4 start-page: 154 year: 1970 ident: 2_CR1 publication-title: Rev. Fr. Autom. Inform. Rech. Opér. – volume: 19 start-page: 790 year: 1994 ident: 2_CR7 publication-title: Math. Oper. Res. doi: 10.1287/moor.19.4.790 – volume: 45 start-page: 1 year: 1999 ident: 2_CR17 publication-title: Optimization doi: 10.1080/02331939908844423 – volume: 17 start-page: 670 year: 1992 ident: 2_CR8 publication-title: Math. Oper. Res. doi: 10.1287/moor.17.3.670 – volume: 18 start-page: 115 year: 1968 ident: 2_CR25 publication-title: Ann. Inst. Fourier doi: 10.5802/aif.280 – volume-title: Quasiconvex Optimization and Location Theory year: 1998 ident: 2_CR16 doi: 10.1007/978-1-4613-3326-5 – volume: 18 start-page: 445 year: 1976 ident: 2_CR24 publication-title: J. Optim. Theory Appl. doi: 10.1007/BF00932654 – volume: 102 start-page: 525 year: 1999 ident: 2_CR29 publication-title: J. Optim. Theory Appl. doi: 10.1023/A:1022693822102 – volume: 2 start-page: 365 year: 2010 ident: 2_CR13 publication-title: Eur. J. Oper. Res. doi: 10.1016/j.ejor.2009.03.045 – volume: 1 start-page: 195 year: 1994 ident: 2_CR28 publication-title: J. Convex Anal. – volume: 7 start-page: 1069 year: 1997 ident: 2_CR9 publication-title: SIAM J. Optim. doi: 10.1137/S1052623495292130 – volume-title: Finite-Dimensional Variational Inequality and Complementarity Problems year: 2003 ident: 2_CR33 – volume: 2 start-page: 305 year: 2001 ident: 2_CR31 publication-title: J. Optim. Theory Appl. doi: 10.1023/A:1012234817482 – volume: 4 start-page: 319 year: 2008 ident: 2_CR10 publication-title: Pac. J. Optim. – volume: 14 start-page: 877 year: 1976 ident: 2_CR2 publication-title: SIAM J. Control Optim. doi: 10.1137/0314056 – volume: 12 start-page: 31 year: 1999 ident: 2_CR4 publication-title: Comput. Optim. Appl. doi: 10.1023/A:1008607511915 – volume: 5 start-page: 777 year: 2010 ident: 2_CR11 publication-title: Optimization doi: 10.1080/02331930902884273 – volume: 355 start-page: 469 year: 2009 ident: 2_CR12 publication-title: J. Convex Anal. – volume: 3 start-page: 627 year: 2003 ident: 2_CR20 publication-title: J. Optim. Theory Appl. doi: 10.1023/A:1023905907248 – volume-title: Variational Analysis year: 1998 ident: 2_CR23 doi: 10.1007/978-3-642-02431-3 – volume-title: Nonlinear Programming: Theory and Algorithms year: 1993 ident: 2_CR19 – volume: 24 start-page: 645 year: 1999 ident: 2_CR3 publication-title: Math. Oper. Res. doi: 10.1287/moor.24.3.645 – volume-title: Microeconomic Theory year: 1995 ident: 2_CR15 – volume: 73 start-page: 451 year: 1992 ident: 2_CR5 publication-title: J. Optim. Theory Appl. doi: 10.1007/BF00940051 – volume: 29 start-page: 1 year: 2004 ident: 2_CR21 publication-title: Math. Oper. Res. doi: 10.1287/moor.1030.0062 – volume: 36 start-page: 351 year: 2006 ident: 2_CR22 publication-title: J. Glob. Optim. doi: 10.1007/s10898-006-9013-4 – volume-title: Optimization and Nonsmooth Analysis year: 1983 ident: 2_CR26 – volume: 10 start-page: 459 year: 2003 ident: 2_CR30 publication-title: J. Convex Anal. |
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| Snippet | In this paper, we propose two interior proximal algorithms inspired by the logarithmic-quadratic proximal method. The first method we propose is for general... |
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| SubjectTerms | Algorithms Applications of Mathematics Calculus of Variations and Optimal Control; Optimization Constraints Convergence Convex analysis Engineering Euclidean space Inequalities Mathematical functions Mathematics Mathematics and Statistics Minimization Operations Research/Decision Theory Optimization Programming Regularization Theory of Computation |
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| Title | Interior Proximal Algorithm for Quasiconvex Programming Problems and Variational Inequalities with Linear Constraints |
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