First and Second Order Optimality Conditions for Nonsmooth Multiobjective Problems with Equilibrium Constraints
In this paper, we first extend the constant positive linear dependence (CPLD) condition in terms of convexificators given by Rimpi and Lalitha [Constraint qualifications in terms of convexificators for nonsmooth programming problems with mixed constraints. Optimization. 2023;72(8):2019-2038] for non...
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| Vydáno v: | Journal of optimization theory and applications Ročník 208; číslo 1; s. 15 |
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| Abstract | In this paper, we first extend the constant positive linear dependence (CPLD) condition in terms of convexificators given by Rimpi and Lalitha [Constraint qualifications in terms of convexificators for nonsmooth programming problems with mixed constraints. Optimization. 2023;72(8):2019-2038] for nonsmooth scalar optimization problems to nonsmooth multiobjective optimization problems with mixed constraints (MOP) which we denote by MOP-CPLD. It also extends the CPLD condition given by Andreani et al. [On the relation between constant positive linear dependence condition and quasinormality constraint qualification. J Optim Theory Appl. 2005;125(2):473-483] involving continuously differentiable functions. We establish a strong Karush-Kuhn-Tucker (KKT) optimality condition to identify local Pareto efficient solutions under the MOP-CPLD framework. We also introduce a suitable CPLD condition for a nonsmooth multiobjective optimization problem with equilibrium constraints in terms of convexificators which is denoted by MOPEC-CPLD. We introduce several nonsmooth strong Pareto stationary points for the MOPEC which extend the notions of strong Pareto stationary points given by Zhang et al. [Constraint qualifications and proper Pareto optimality conditions for multiobjective problems with equilibrium constraints. J Optim Theory Appl. 2018;176:763-782] for continuously differentiable functions. We provide necessary and sufficient optimality conditions to identify a stationary point as a Pareto efficient solution of the MOPEC under the MOPEC-CPLD condition. Further, we introduce Abadie constraint qualifications for MOPEC which is denoted by MOPEC-SOACQ in terms of Clarke generalized derivative and second-order upper directional derivative given by Páles and Zeidan. This notion utilizes second-order ACQ given by Anchal and Lalita [Second-order optimality conditions for locally Lipschitz vector optimization problems. Optimization. 2023;1-20] for multiobjective optimization problems. We derive second-order necessary optimality conditions in both the primal and the dual forms to identify weak Pareto efficient solutions and strict Pareto efficient solutions of order two for MOPEC by utilizing MOPEC-SOACQ. We give some applications of the results in interval-valued multiobjective optimization problems with equilibrium constraints and in portfolio optimization. |
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| AbstractList | In this paper, we first extend the constant positive linear dependence (CPLD) condition in terms of convexificators given by Rimpi and Lalitha [Constraint qualifications in terms of convexificators for nonsmooth programming problems with mixed constraints. Optimization. 2023;72(8):2019-2038] for nonsmooth scalar optimization problems to nonsmooth multiobjective optimization problems with mixed constraints (MOP) which we denote by MOP-CPLD. It also extends the CPLD condition given by Andreani et al. [On the relation between constant positive linear dependence condition and quasinormality constraint qualification. J Optim Theory Appl. 2005;125(2):473-483] involving continuously differentiable functions. We establish a strong Karush-Kuhn-Tucker (KKT) optimality condition to identify local Pareto efficient solutions under the MOP-CPLD framework. We also introduce a suitable CPLD condition for a nonsmooth multiobjective optimization problem with equilibrium constraints in terms of convexificators which is denoted by MOPEC-CPLD. We introduce several nonsmooth strong Pareto stationary points for the MOPEC which extend the notions of strong Pareto stationary points given by Zhang et al. [Constraint qualifications and proper Pareto optimality conditions for multiobjective problems with equilibrium constraints. J Optim Theory Appl. 2018;176:763-782] for continuously differentiable functions. We provide necessary and sufficient optimality conditions to identify a stationary point as a Pareto efficient solution of the MOPEC under the MOPEC-CPLD condition. Further, we introduce Abadie constraint qualifications for MOPEC which is denoted by MOPEC-SOACQ in terms of Clarke generalized derivative and second-order upper directional derivative given by Páles and Zeidan. This notion utilizes second-order ACQ given by Anchal and Lalita [Second-order optimality conditions for locally Lipschitz vector optimization problems. Optimization. 2023;1-20] for multiobjective optimization problems. We derive second-order necessary optimality conditions in both the primal and the dual forms to identify weak Pareto efficient solutions and strict Pareto efficient solutions of order two for MOPEC by utilizing MOPEC-SOACQ. We give some applications of the results in interval-valued multiobjective optimization problems with equilibrium constraints and in portfolio optimization. |
| ArticleNumber | 15 |
| Author | Laha, Vivek Anshika Sachan, Prachi |
| Author_xml | – sequence: 1 givenname: Prachi surname: Sachan fullname: Sachan, Prachi – sequence: 2 givenname: Vivek orcidid: 0000-0002-0584-9500 surname: Laha fullname: Laha, Vivek – sequence: 3 surname: Anshika fullname: Anshika |
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| Cites_doi | 10.1016/j.cam.2024.116483 10.1080/02331934.2014.987776 10.1007/s10287-023-00461-3 10.1007/s10957-004-1176-x 10.1007/s10589-025-00663-2 10.1017/CBO9780511983658 10.1016/j.orl.2015.12.007 10.1016/j.jmaa.2005.02.011 10.1023/A:1014853129484 10.1016/j.jmaa.2004.10.032 10.1007/978-3-030-52119-6_12 10.1007/BF03322575 10.1007/s12190-019-01274-x 10.1186/s13660-022-02866-1 10.1007/s10479-025-06627-3 10.1051/ro/2018084 10.1007/978-981-10-4774-9 10.1016/j.fss.2025.109416 10.1080/0233193031000120020 10.3390/math10193516 10.1007/978-981-99-0597-3_20 10.1007/s10957-007-9209-x 10.1007/s41478-023-00621-3 10.1007/s10107-007-0172-y 10.1007/s10957-004-1861-9 10.1016/j.ejor.2012.11.005 10.1287/moor.25.1.1.15213 10.1080/02331934.2023.2169046 10.1080/02331934.2019.1591406 10.1080/02331934.2018.1545122 10.1007/s10957-020-01688-9 10.1007/s10898-017-0556-3 10.1137/S0363012996311095 10.1007/s10957-016-0885-2 10.1007/s10957-006-9155-z 10.1007/s10107-010-0342-1 10.1080/02331930410001661505 10.1080/02331934.2021.2016752 10.1080/0233193031000149894 10.1007/s10957-012-0084-8 10.57262/die/1371043981 10.1137/S0363012992229653 10.1080/02331934.2022.2045987 10.1137/0805033 10.1007/s40314-025-03244-5 10.1051/ro/2023044 10.1007/s10957-018-1235-3 10.1080/02331930500342591 10.1023/A:1021790120780 10.18576/amisl/070103 |
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| References | S Treanţă (2853_CR53) 2022; 10 2853_CR1 2853_CR49 2853_CR47 X Zhao (2853_CR59) 2025; 91 H Rehman (2853_CR54) 2025; 44 2853_CR5 G Giorgi (2853_CR23) 2010; 52 P Michel (2853_CR38) 1992; 5 2853_CR41 BS Mordukhovich (2853_CR39) 2009; 117 2853_CR40 2853_CR7 L Guo (2853_CR22) 2013; 156 V Jeyakumar (2853_CR24) 1999; 101 Y Pandey (2853_CR42) 2016; 171 TQ Bao (2853_CR6) 2007; 135 JP Penot (2853_CR44) 1998; 37 R Andreani (2853_CR2) 2005; 125 DV Luu (2853_CR37) 2018; 70 JS Trieman (2853_CR51) 1995; 5 J Dutta (2853_CR13) 2004; 53 2853_CR36 V Chankong (2853_CR9) 1983 M Feng (2853_CR20) 2018; 67 ML Flegel (2853_CR19) 2005; 310 A Ansari Ardali (2853_CR3) 2006; 65 S Dempe (2853_CR15) 2012; 131 P Zhang (2853_CR57) 2018; 176 Y Pandey (2853_CR43) 2016; 44 ML Flegel (2853_CR17) 2005; 124 Z Páles (2853_CR45) 1994; 32 XF Li (2853_CR33) 2006; 131 A Ansari Ardali (2853_CR4) 2022; 13 YC Duan (2853_CR16) 2007; 8 2853_CR21 2853_CR26 JJ Ye (2853_CR55) 2005; 307 S Dempe (2853_CR11) 2003; 52 ML Flegel (2853_CR18) 2005; 54 B Kohli (2853_CR27) 2019; 53 KK Lai (2853_CR29) 2022; 2022 S Dempe (2853_CR14) 2023; 57 ZY Peng (2853_CR46) 2025; 515 P Zhang (2853_CR58) 2019; 68 ZQ Luo (2853_CR32) 1996 2853_CR28 KV Singh (2853_CR48) 2019; 7 V Laha (2853_CR35) 2023; 20 LT Tung (2853_CR52) 2020; 62 H Scheel (2853_CR50) 2000; 25 FH Clarke (2853_CR8) 1983 J Dutta (2853_CR12) 2002; 113 L Lafhim (2853_CR30) 2023; 72 V Jeyakumar (2853_CR25) 2008 V Laha (2853_CR34) 2024; 32 GH Lin (2853_CR31) 2013; 226 X Zhang (2853_CR56) 2025; 462 E Constantin (2853_CR10) 2020; 186 |
| References_xml | – volume-title: Optimization and nonsmooth analysis year: 1983 ident: 2853_CR8 – volume: 462 year: 2025 ident: 2853_CR56 publication-title: J. Comput. Appl. Math. doi: 10.1016/j.cam.2024.116483 – volume: 65 start-page: 67 issue: 1 year: 2006 ident: 2853_CR3 publication-title: Optimization doi: 10.1080/02331934.2014.987776 – volume-title: Nonsmooth vector functions and continuous optimization year: 2008 ident: 2853_CR25 – volume: 20 start-page: 30 issue: 1 year: 2023 ident: 2853_CR35 publication-title: Comput. Manag. Sci. doi: 10.1007/s10287-023-00461-3 – volume: 124 start-page: 595 year: 2005 ident: 2853_CR17 publication-title: J. Optim. Theory Appl. doi: 10.1007/s10957-004-1176-x – volume: 91 start-page: 27 issue: 1 year: 2025 ident: 2853_CR59 publication-title: Comput. Optim. Appl. doi: 10.1007/s10589-025-00663-2 – volume: 13 start-page: 2185 issue: 2 year: 2022 ident: 2853_CR4 publication-title: Int J Nonlinear Anal Appl. – volume-title: Mathematical Programs with Equilibrium Constraints year: 1996 ident: 2853_CR32 doi: 10.1017/CBO9780511983658 – volume: 44 start-page: 148 issue: 1 year: 2016 ident: 2853_CR43 publication-title: Oper. Res. Lett. doi: 10.1016/j.orl.2015.12.007 – volume: 310 start-page: 286 issue: 1 year: 2005 ident: 2853_CR19 publication-title: J. Math. Anal. Appl. doi: 10.1016/j.jmaa.2005.02.011 – volume: 113 start-page: 41 issue: 1 year: 2002 ident: 2853_CR12 publication-title: J. Optim. Theory Appl. doi: 10.1023/A:1014853129484 – volume: 307 start-page: 350 issue: 1 year: 2005 ident: 2853_CR55 publication-title: J. Math. Anal. Appl. doi: 10.1016/j.jmaa.2004.10.032 – ident: 2853_CR26 doi: 10.1007/978-3-030-52119-6_12 – volume: 52 start-page: 73 year: 2010 ident: 2853_CR23 publication-title: SeMA Journal. doi: 10.1007/BF03322575 – volume: 62 start-page: 67 year: 2020 ident: 2853_CR52 publication-title: J. Appl. Math. Comput. doi: 10.1007/s12190-019-01274-x – volume: 2022 start-page: 128 issue: 1 year: 2022 ident: 2853_CR29 publication-title: J Inequalities Appl. doi: 10.1186/s13660-022-02866-1 – ident: 2853_CR28 doi: 10.1007/s10479-025-06627-3 – volume: 53 start-page: 1617 issue: 5 year: 2019 ident: 2853_CR27 publication-title: RAIRO Oper Res. doi: 10.1051/ro/2018084 – ident: 2853_CR41 – ident: 2853_CR5 doi: 10.1007/978-981-10-4774-9 – ident: 2853_CR49 – ident: 2853_CR7 – volume: 515 year: 2025 ident: 2853_CR46 publication-title: Fuzzy Sets Syst. doi: 10.1016/j.fss.2025.109416 – volume-title: Multiobjective Decision Making: Theory and Methodology year: 1983 ident: 2853_CR9 – ident: 2853_CR21 doi: 10.1080/0233193031000120020 – volume: 10 start-page: 3516 issue: 19 year: 2022 ident: 2853_CR53 publication-title: Mathematics. doi: 10.3390/math10193516 – ident: 2853_CR36 doi: 10.1007/978-981-99-0597-3_20 – volume: 135 start-page: 179 issue: 2 year: 2007 ident: 2853_CR6 publication-title: J. Optim. Theory Appl. doi: 10.1007/s10957-007-9209-x – volume: 32 start-page: 219 year: 2024 ident: 2853_CR34 publication-title: J Anal. doi: 10.1007/s41478-023-00621-3 – volume: 117 start-page: 331 issue: 1 year: 2009 ident: 2853_CR39 publication-title: Math. Program. doi: 10.1007/s10107-007-0172-y – volume: 125 start-page: 473 issue: 2 year: 2005 ident: 2853_CR2 publication-title: J. Optim. Theory Appl. doi: 10.1007/s10957-004-1861-9 – volume: 226 start-page: 461 issue: 3 year: 2013 ident: 2853_CR31 publication-title: Eur. J. Oper. Res. doi: 10.1016/j.ejor.2012.11.005 – volume: 25 start-page: 1 year: 2000 ident: 2853_CR50 publication-title: Math. Oper. Res. doi: 10.1287/moor.25.1.1.15213 – ident: 2853_CR40 – ident: 2853_CR1 doi: 10.1080/02331934.2023.2169046 – volume: 68 start-page: 1245 issue: 6 year: 2019 ident: 2853_CR58 publication-title: Optimization doi: 10.1080/02331934.2019.1591406 – volume: 67 start-page: 2117 issue: 12 year: 2018 ident: 2853_CR20 publication-title: Optimization doi: 10.1080/02331934.2018.1545122 – volume: 186 start-page: 50 issue: 1 year: 2020 ident: 2853_CR10 publication-title: J. Optim. Theory Appl. doi: 10.1007/s10957-020-01688-9 – volume: 70 start-page: 437 year: 2018 ident: 2853_CR37 publication-title: J. Global Optim. doi: 10.1007/s10898-017-0556-3 – volume: 8 start-page: 12 issue: 1 year: 2007 ident: 2853_CR16 publication-title: Rose-Hulman Undergraduate Mathematics Journal. – volume: 37 start-page: 303 issue: 1 year: 1998 ident: 2853_CR44 publication-title: SIAM J. Control. Optim. doi: 10.1137/S0363012996311095 – volume: 171 start-page: 694 year: 2016 ident: 2853_CR42 publication-title: J. Optim. Theory Appl. doi: 10.1007/s10957-016-0885-2 – volume: 131 start-page: 429 issue: 3 year: 2006 ident: 2853_CR33 publication-title: J. Optim. Theory Appl. doi: 10.1007/s10957-006-9155-z – volume: 131 start-page: 37 year: 2012 ident: 2853_CR15 publication-title: Math. Program. doi: 10.1007/s10107-010-0342-1 – volume: 53 start-page: 77 issue: 1 year: 2004 ident: 2853_CR13 publication-title: Optimization doi: 10.1080/02331930410001661505 – volume: 72 start-page: 1363 issue: 5 year: 2023 ident: 2853_CR30 publication-title: Optimization doi: 10.1080/02331934.2021.2016752 – volume: 52 start-page: 333 issue: 3 year: 2003 ident: 2853_CR11 publication-title: Optimization doi: 10.1080/0233193031000149894 – volume: 156 start-page: 600 year: 2013 ident: 2853_CR22 publication-title: J. Optim. Theory Appl. doi: 10.1007/s10957-012-0084-8 – volume: 5 start-page: 433 issue: 2 year: 1992 ident: 2853_CR38 publication-title: Differential Integral Equations doi: 10.57262/die/1371043981 – volume: 32 start-page: 1476 issue: 5 year: 1994 ident: 2853_CR45 publication-title: SIAM J. Control. Optim. doi: 10.1137/S0363012992229653 – ident: 2853_CR47 doi: 10.1080/02331934.2022.2045987 – volume: 5 start-page: 670 issue: 3 year: 1995 ident: 2853_CR51 publication-title: SIAM J. Optim. doi: 10.1137/0805033 – volume: 44 start-page: 274 issue: 6 year: 2025 ident: 2853_CR54 publication-title: Comput Appl Math. doi: 10.1007/s40314-025-03244-5 – volume: 57 start-page: 1009 issue: 3 year: 2023 ident: 2853_CR14 publication-title: RAIRO Oper Res. doi: 10.1051/ro/2023044 – volume: 176 start-page: 763 year: 2018 ident: 2853_CR57 publication-title: J. Optim. Theory Appl. doi: 10.1007/s10957-018-1235-3 – volume: 54 start-page: 517 issue: 6 year: 2005 ident: 2853_CR18 publication-title: Optimization doi: 10.1080/02331930500342591 – volume: 101 start-page: 599 issue: 3 year: 1999 ident: 2853_CR24 publication-title: J. Optim. Theory Appl. doi: 10.1023/A:1021790120780 – volume: 7 start-page: 17 year: 2019 ident: 2853_CR48 publication-title: Appl. Math. Inf. Sci. Lett. doi: 10.18576/amisl/070103 |
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