A proximal point method for difference of convex functions in multi-objective optimization with application to group dynamic problems

We consider the constrained multi-objective optimization problem of finding Pareto critical points of difference of convex functions. The new approach proposed by Bento et al. (SIAM J Optim 28:1104–1120, 2018) to study the convergence of the proximal point method is applied. Our method minimizes at...

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Published in:	Computational optimization and applications Vol. 75; no. 1; pp. 263 - 290
Main Authors:	de Carvalho Bento, Glaydston, Bitar, Sandro Dimy Barbosa, da Cruz Neto, João Xavier, Soubeyran, Antoine, de Oliveira Souza, João Carlos
Format:	Journal Article
Language:	English
Published:	New York Springer US 01.01.2020 Springer Nature B.V Springer Verlag
Subjects:	Ascent Convex analysis Convex and Discrete Geometry Critical point Economics and Finance Goal programming Group dynamics Humanities and Social Sciences Iterative methods Management Science Mathematical analysis Mathematics Mathematics and Statistics Multiple objective analysis Operations Research Operations Research/Decision Theory Optimization Pareto optimization Statistics Multi-objective programming Behavioral sciences Proximal point method DC function Variational rationality
ISSN:	0926-6003, 1573-2894
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Abstract	We consider the constrained multi-objective optimization problem of finding Pareto critical points of difference of convex functions. The new approach proposed by Bento et al. (SIAM J Optim 28:1104–1120, 2018) to study the convergence of the proximal point method is applied. Our method minimizes at each iteration a convex approximation instead of the (non-convex) objective function constrained to a possibly non-convex set which assures the vector improving process. The motivation comes from the famous Group Dynamic problem in Behavioral Sciences where, at each step, a group of (possible badly informed) agents tries to increase his joint payoff, in order to be able to increase the payoff of each of them. In this way, at each step, this ascent process guarantees the stability of the group. Some encouraging preliminary numerical results are reported.
AbstractList	We consider the constrained multi-objective optimization problem of finding Pareto critical points of difference of convex functions. The new approach proposed by Bento et al. (SIAM J Optim 28:1104–1120, 2018) to study the convergence of the proximal point method is applied. Our method minimizes at each iteration a convex approximation instead of the (non-convex) objective function constrained to a possibly non-convex set which assures the vector improving process. The motivation comes from the famous Group Dynamic problem in Behavioral Sciences where, at each step, a group of (possible badly informed) agents tries to increase his joint payoff, in order to be able to increase the payoff of each of them. In this way, at each step, this ascent process guarantees the stability of the group. Some encouraging preliminary numerical results are reported.
Author	Bitar, Sandro Dimy Barbosa de Oliveira Souza, João Carlos Soubeyran, Antoine da Cruz Neto, João Xavier de Carvalho Bento, Glaydston
Author_xml	– sequence: 1 givenname: Glaydston surname: de Carvalho Bento fullname: de Carvalho Bento, Glaydston organization: IME, Federal University of Goiás – sequence: 2 givenname: Sandro Dimy Barbosa surname: Bitar fullname: Bitar, Sandro Dimy Barbosa organization: ICE, Federal University of Amazonas – sequence: 3 givenname: João Xavier surname: da Cruz Neto fullname: da Cruz Neto, João Xavier organization: CCN, DM, Federal University of Piauí – sequence: 4 givenname: Antoine surname: Soubeyran fullname: Soubeyran, Antoine organization: CNRS and EHESS, Aix-Marseille University (Aix-Marseille School of Economics) – sequence: 5 givenname: João Carlos orcidid: 0000-0003-4053-8211 surname: de Oliveira Souza fullname: de Oliveira Souza, João Carlos email: joaocos.mat@ufpi.edu.br organization: CCN, DM, Federal University of Piauí
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Cites_doi	10.1016/j.cam.2004.06.018 10.1016/0022-247X(92)90336-C 10.1016/j.ejor.2015.06.016 10.1007/s10957-013-0327-3 10.1007/s11228-014-0279-2 10.1080/02331934.2010.522710 10.1177/001872674700100103 10.1016/j.ejor.2014.01.022 10.1007/s10898-015-0367-3 10.1080/02331931003770411 10.1137/S1052623403429093 10.1007/978-3-540-24828-6 10.4064/ap87-0-2 10.1007/BF00935364 10.1007/s10957-015-0711-2 10.1137/060655183 10.1007/s10898-014-0159-1 10.1007/s11228-015-0319-6 10.1137/S1052623494274313 10.1023/B:COAP.0000018877.86161.8b 10.1137/08071692X 10.1007/3-540-31246-3 10.1007/s10957-010-9667-4 10.1590/0101-7438.2014.034.03.0585 10.1007/BF01580762 10.1007/978-3-319-92775-6 10.1090/S0002-9947-1975-0367131-6 10.1007/s10898-015-0282-7 10.1007/s10957-015-0847-0 10.2140/pjm.1959.9.707 10.1016/j.ejor.2014.01.002 10.1007/s10898-009-9486-z 10.1007/s10589-012-9494-7 10.1137/0314056 10.1016/j.ejor.2011.05.006 10.1007/s101070050050 10.1016/0022-247X(82)90226-8 10.1016/0377-2217(80)90142-3 10.1080/02331934.2011.564623 10.1007/978-3-642-45610-7_3 10.1007/3-540-31247-1 10.1023/B:JOTA.0000012735.86699.a1 10.1016/j.ejor.2006.09.070 10.1080/02331930903500282 10.24033/bsmf.1625 10.1137/120866415 10.1137/16M107534X 10.1023/A:1017535424813 10.1007/s10589-017-9954-1 10.1016/j.ejor.2016.05.026 10.1137/1.9781611971309 10.1093/oso/9780195135008.001.0001 10.1007/s10479-018-3104-8 10.1016/S0304-0208(08)72402-2
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Keywords	Multi-objective programming Behavioral sciences Proximal point method DC function Variational rationality
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References	Holmberg, Tuy (CR31) 1999; 85 Bento, Soubeyran (CR7) 2015; 166 Bento, Cruz Neto, Oliveira, Soubeyran (CR6) 2014; 235 Ji, Goh, De Souza (CR34) 2016; 169 Thibault (CR64) 1982; 86 Bello Cruz (CR3) 2013; 23 Dinh, Strodiot, Nguyen (CR20) 2010; 48 Hartman (CR29) 1959; 9 Apolinário, Papa Quiroz, Oliveira (CR1) 2016; 64 Burke, Ferris, Qian (CR12) 1992; 166 Martinet (CR40) 1970; 4 Bento, Cruz Neto, López, Soubeyran, Souza (CR4) 2018; 28 Jahn (CR33) 2004 Souza, Oliveira (CR60) 2015; 63 Tuy, Horst (CR65) 1988; 41 Flores-Bazán, Oettli (CR23) 2001; 108 Qu, Liu, Goh, Li, Ji (CR51) 2014; 235 Bento, Cruz Neto, Soubeyran (CR5) 2014; 22 Graña Drummond, Iusem (CR26) 2004; 28 Ceng, Mordukhovich, Yao (CR14) 2010; 146 Minami (CR42) 1983; 41 Muu, Quoc (CR49) 2010; 59 Lewin (CR36) 1964 Guo, Li (CR28) 2014; 162 Fukuda, Graña Drummond (CR25) 2014; 34 Fukuda, Graña Drummond (CR24) 2011; 60 Bolte, Danilidis, Lewis, Shiota (CR9) 2005; 87 Brito, Cruz Neto, Santos, Souza (CR11) 2017; 256 Miettinen (CR41) 1999 Huang, Yang (CR32) 2004; 120 Rockafellar (CR53) 1976; 14 Villacorta, Oliveira (CR66) 2011; 214 Graña Drummond, Svaiter (CR27) 2005; 175 CR18 Bento, Soubeyran (CR8) 2015; 23 CR59 Mordukhovich (CR47) 2006 CR58 Fliege, Graña Drummond, Svaiter (CR22) 2009; 20 CR57 CR56 Hiriart-Urruty (CR30) 1986; 256 CR55 Cruz Neto, Silva, Ferreira, Lopes (CR19) 2013; 54 Lewin (CR35) 1947; 1 Bačák, Borwein (CR2) 2011; 60 Mai, Luu (CR39) 2018; 2 Ceng, Yao (CR13) 2007; 183 Clarke (CR16) 1975; 205 Moreno, Oliveira, Soubeyran (CR44) 2012; 61 Ferrer, Bagirov, Beliakov (CR21) 2015; 61 Luc, Tan, Tinh (CR37) 1998; 23 Qu, Goh, Ji, De Souza (CR52) 2015; 247 Wen, Chen, Pong (CR67) 2018; 69 Bonnel, Iusem, Svaiter (CR10) 2005; 15 Ross, Soland (CR54) 1980; 4 Clarke (CR17) 1990 Sun, Sampaio, Candido (CR61) 2003; 21 Mordukhovich (CR46) 2006 Choung, Mordukhovich, Yao (CR15) 2011; 12 CR62 Tao, An (CR63) 1998; 8 Moreau (CR43) 1965; 93 Mordukhovich (CR48) 2018 Poole, Van de Ven (CR50) 2004 Luc (CR38) 1989 Maingé, Moudafi (CR45) 2008; 19 XL Guo (139_CR28) 2014; 162 H Tuy (139_CR65) 1988; 41 DT Luc (139_CR38) 1989 BS Mordukhovich (139_CR48) 2018 HCF Apolinário (139_CR1) 2016; 64 LC Ceng (139_CR13) 2007; 183 K Lewin (139_CR35) 1947; 1 JB Hiriart-Urruty (139_CR30) 1986; 256 Y Ji (139_CR34) 2016; 169 J Fliege (139_CR22) 2009; 20 TD Choung (139_CR15) 2011; 12 GC Bento (139_CR7) 2015; 166 JX Cruz Neto (139_CR19) 2013; 54 GC Bento (139_CR4) 2018; 28 H Bonnel (139_CR10) 2005; 15 KDV Villacorta (139_CR66) 2011; 214 BS Mordukhovich (139_CR47) 2006 F Flores-Bazán (139_CR23) 2001; 108 P-E Maingé (139_CR45) 2008; 19 S Qu (139_CR52) 2015; 247 K Holmberg (139_CR31) 1999; 85 FG Moreno (139_CR44) 2012; 61 LD Muu (139_CR49) 2010; 59 139_CR55 TT Mai (139_CR39) 2018; 2 LM Graña Drummond (139_CR26) 2004; 28 M Bačák (139_CR2) 2011; 60 139_CR18 MS Poole (139_CR50) 2004 AS Brito (139_CR11) 2017; 256 GC Bento (139_CR6) 2014; 235 EH Fukuda (139_CR25) 2014; 34 139_CR58 139_CR59 139_CR56 139_CR57 RT Rockafellar (139_CR53) 1976; 14 W Sun (139_CR61) 2003; 21 EH Fukuda (139_CR24) 2011; 60 XX Huang (139_CR32) 2004; 120 DT Luc (139_CR37) 1998; 23 139_CR62 N Dinh (139_CR20) 2010; 48 P Hartman (139_CR29) 1959; 9 J Jahn (139_CR33) 2004 S Qu (139_CR51) 2014; 235 LM Graña Drummond (139_CR27) 2005; 175 PD Tao (139_CR63) 1998; 8 A Ferrer (139_CR21) 2015; 61 GT Ross (139_CR54) 1980; 4 M Minami (139_CR42) 1983; 41 JY Bello Cruz (139_CR3) 2013; 23 JJ Moreau (139_CR43) 1965; 93 JV Burke (139_CR12) 1992; 166 FH Clarke (139_CR16) 1975; 205 FH Clarke (139_CR17) 1990 B Martinet (139_CR40) 1970; 4 GC Bento (139_CR8) 2015; 23 JCO Souza (139_CR60) 2015; 63 B Wen (139_CR67) 2018; 69 K Lewin (139_CR36) 1964 KM Miettinen (139_CR41) 1999 GC Bento (139_CR5) 2014; 22 LC Ceng (139_CR14) 2010; 146 BS Mordukhovich (139_CR46) 2006 J Bolte (139_CR9) 2005; 87 L Thibault (139_CR64) 1982; 86
References_xml	– volume: 175 start-page: 395 year: 2005 end-page: 414 ident: CR27 article-title: A steepest descent method for vector optimization publication-title: J. Comput. Appl. Math. doi: 10.1016/j.cam.2004.06.018 – volume: 166 start-page: 199 year: 1992 end-page: 213 ident: CR12 article-title: On the Clarke subdifferential of the distance function of a closed set publication-title: J. Math. Anal. Appl. doi: 10.1016/0022-247X(92)90336-C – volume: 247 start-page: 359 year: 2015 end-page: 365 ident: CR52 article-title: A new algorithm for linearly constrained c-convex vector optimization with a supply chain network risk application publication-title: Eur. J. Oper. Res. doi: 10.1016/j.ejor.2015.06.016 – volume: 12 start-page: 257 year: 2011 end-page: 286 ident: CR15 article-title: Hybrid approximate proximal algorithms for efficient solutions in vector optimization publication-title: J. Nonlinear Convex Anal. – volume: 162 start-page: 821 year: 2014 end-page: 844 ident: CR28 article-title: Optimality conditions for vector optimization problems with difference of convex maps publication-title: J. Optim. Theory Appl. doi: 10.1007/s10957-013-0327-3 – volume: 22 start-page: 557 year: 2014 end-page: 573 ident: CR5 article-title: A proximal point-type method for multicriteria optimization publication-title: Set-Valued Var. Anal. doi: 10.1007/s11228-014-0279-2 – volume: 60 start-page: 1009 year: 2011 end-page: 1021 ident: CR24 article-title: On the convergence of the projected gradient method for vector optimization publication-title: Optimization doi: 10.1080/02331934.2010.522710 – volume: 1 start-page: 5 year: 1947 end-page: 41 ident: CR35 article-title: Frontiers in group dynamics: concept, method and reality in social science; social equilibria and social change publication-title: Hum. Relat. doi: 10.1177/001872674700100103 – volume: 235 start-page: 503 year: 2014 end-page: 510 ident: CR51 article-title: Nonsmooth multiobjective programming with quasi-Newton methods publication-title: Eur. J. Oper. Res. doi: 10.1016/j.ejor.2014.01.022 – volume: 64 start-page: 79 year: 2016 end-page: 96 ident: CR1 article-title: A scalarization proximal point method for quasiconvex multiobjective minimization publication-title: J. Glob. Optim. doi: 10.1007/s10898-015-0367-3 – volume: 60 start-page: 961 year: 2011 end-page: 978 ident: CR2 article-title: On difference convexity of locally Lipschitz functions publication-title: Optimization doi: 10.1080/02331931003770411 – volume: 15 start-page: 953 year: 2005 end-page: 970 ident: CR10 article-title: Proximal methods in vector optimization publication-title: SIAM J. Optim. doi: 10.1137/S1052623403429093 – year: 2004 ident: CR33 publication-title: Vector Optimization: Theory, Applications and Extensions doi: 10.1007/978-3-540-24828-6 – volume: 87 start-page: 13 year: 2005 end-page: 25 ident: CR9 article-title: Clarke critical values of subanalytic Lipschitz continuous functions publication-title: Ann. Polon. Math. doi: 10.4064/ap87-0-2 – volume: 41 start-page: 451 year: 1983 end-page: 461 ident: CR42 article-title: Weak Pareto-optimal necessary conditions in a nondifferentiable multiobjective program on a Banach space publication-title: J. Optim. Theory Appl. doi: 10.1007/BF00935364 – volume: 166 start-page: 172 year: 2015 end-page: 187 ident: CR7 article-title: Generalized inexact proximal algorithms: routine’s formation with resistance to change, following worthwhile changes publication-title: J. Optim. Theory Appl. doi: 10.1007/s10957-015-0711-2 – volume: 19 start-page: 397 year: 2008 end-page: 413 ident: CR45 article-title: Convergence of new inertial proximal methods for DC programming publication-title: SIAM J. Optim. doi: 10.1137/060655183 – volume: 61 start-page: 71 year: 2015 end-page: 89 ident: CR21 article-title: Solving DC programs using the cutting angle method publication-title: J. Glob. Optim. doi: 10.1007/s10898-014-0159-1 – volume: 23 start-page: 501 year: 2015 end-page: 517 ident: CR8 article-title: A generalized inexact proximal point method for nonsmooth functions that satisfies Kurdyka–Łojasiewicz inequality publication-title: Set-Valued Var. Anal. doi: 10.1007/s11228-015-0319-6 – volume: 8 start-page: 476 year: 1998 end-page: 505 ident: CR63 article-title: A DC optimization algorithm for solving the trust region subproblem publication-title: SIAM J. Optim. doi: 10.1137/S1052623494274313 – volume: 28 start-page: 5 year: 2004 end-page: 29 ident: CR26 article-title: A projected gradient method for vector optimization problems publication-title: Comput. Optim. Appl. doi: 10.1023/B:COAP.0000018877.86161.8b – ident: CR58 – volume: 20 start-page: 602 issue: 2 year: 2009 end-page: 626 ident: CR22 article-title: Newton’s method for multiobjective optimization publication-title: SIAM J. Optim. doi: 10.1137/08071692X – year: 2006 ident: CR47 publication-title: Variational Analysis and Generalized Differentiation. II. Applications, Grundlehren der Mathematischen Wissenschaften doi: 10.1007/3-540-31246-3 – volume: 146 start-page: 267 year: 2010 end-page: 303 ident: CR14 article-title: Hybrid approximate proximal method with auxiliary variational inequality for vector optimization publication-title: J. Optim. Theory Appl. doi: 10.1007/s10957-010-9667-4 – volume: 34 start-page: 585 year: 2014 end-page: 620 ident: CR25 article-title: A survey on multiobjective descent methods publication-title: Pesqui. Oper. doi: 10.1590/0101-7438.2014.034.03.0585 – volume: 41 start-page: 161 year: 1988 end-page: 183 ident: CR65 article-title: Convergence and restart in branch-and-bound algorithms for global optimization. Application to concave minimization and dc optimization problems publication-title: Math. Program. doi: 10.1007/BF01580762 – year: 2018 ident: CR48 publication-title: Variational Analysis and Applications doi: 10.1007/978-3-319-92775-6 – volume: 205 start-page: 247 year: 1975 end-page: 262 ident: CR16 article-title: Generalized gradients and applications publication-title: Trans. Am. Math. Soc. doi: 10.1090/S0002-9947-1975-0367131-6 – volume: 63 start-page: 797 year: 2015 end-page: 810 ident: CR60 article-title: A proximal point algorithm for DC functions on Hadamard manifolds publication-title: J. Glob. Optim. doi: 10.1007/s10898-015-0282-7 – volume: 169 start-page: 280 year: 2016 end-page: 289 ident: CR34 article-title: Proximal point algorithms for multi-criteria optimization with the difference of convex objective functions publication-title: J. Optim. Theory Appl. doi: 10.1007/s10957-015-0847-0 – volume: 9 start-page: 707 year: 1959 end-page: 713 ident: CR29 article-title: On functions representable as a difference of convex functions publication-title: Pac. J. Math. doi: 10.2140/pjm.1959.9.707 – ident: CR57 – volume: 235 start-page: 494 year: 2014 end-page: 502 ident: CR6 article-title: The self regulation problem as an inexact steepest descent method for multicriteria optimization publication-title: Eur. J. Oper. Res. doi: 10.1016/j.ejor.2014.01.002 – volume: 23 start-page: 107 year: 1998 end-page: 127 ident: CR37 article-title: Convex vector functions and their subdifferential publication-title: Acta Math. Vietnam – volume: 48 start-page: 183 year: 2010 end-page: 208 ident: CR20 article-title: Duality and optimality conditions for generalized equilibrium problems involving DC functions publication-title: Glob. Optim. doi: 10.1007/s10898-009-9486-z – ident: CR18 – year: 2004 ident: CR50 publication-title: Handbook of Organizational Change and Innovation – volume: 54 start-page: 461 year: 2013 end-page: 472 ident: CR19 article-title: A subgradient method for multiobjective optimization publication-title: Comput. Optim. Appl. doi: 10.1007/s10589-012-9494-7 – volume: 14 start-page: 877 year: 1976 end-page: 898 ident: CR53 article-title: Monotone operators and the proximal point algorithm publication-title: SIAM J. Control. Optim. doi: 10.1137/0314056 – year: 1989 ident: CR38 publication-title: Theory of Vector Optimization. Lecture Notes in Economics and Mathematical Systems – year: 1964 ident: CR36 publication-title: Field Theory in Social Science. Harper Torchbooks – year: 1999 ident: CR41 publication-title: Nonlinear Multiobjective Optimization – volume: 214 start-page: 485 year: 2011 end-page: 492 ident: CR66 article-title: An interior proximal method in vector optimization publication-title: Eur. J. Oper. Res. doi: 10.1016/j.ejor.2011.05.006 – volume: 85 start-page: 157 year: 1999 end-page: 179 ident: CR31 article-title: A production–transportation problem with stochastic demand and concave production costs publication-title: Math. Program. doi: 10.1007/s101070050050 – volume: 21 start-page: 451 year: 2003 end-page: 462 ident: CR61 article-title: Proximal point algorithm for minimization of DC Functions publication-title: J. Comput. Math. – ident: CR56 – volume: 86 start-page: 319 year: 1982 end-page: 344 ident: CR64 article-title: Subdifferentials of nonconvex vector-valued functions publication-title: J. Math. Anal. Appl. doi: 10.1016/0022-247X(82)90226-8 – volume: 4 start-page: 307 year: 1980 end-page: 321 ident: CR54 article-title: A multicriteria approach to the location of public facilities publication-title: Eur. J. Oper. Res. doi: 10.1016/0377-2217(80)90142-3 – volume: 61 start-page: 1383 year: 2012 end-page: 1403 ident: CR44 article-title: A proximal point algorithm with quasi distance. Application to habit’s formation publication-title: Optimization doi: 10.1080/02331934.2011.564623 – volume: 256 start-page: 37 year: 1986 end-page: 70 ident: CR30 article-title: Generalized differentiabity, duality and optimization for problems dealing with difference of convex functions publication-title: Convex. Dual. Optim. Lect. Notes Econ. Math. Syst. doi: 10.1007/978-3-642-45610-7_3 – year: 2006 ident: CR46 publication-title: Variational Analysis and Generalized Differentiation. I. Basic Theory, Grundlehren der Mathematischen Wissenschaften doi: 10.1007/3-540-31247-1 – volume: 120 start-page: 111 year: 2004 end-page: 127 ident: CR32 article-title: Duality for multiobjective optimization via nonlinear Lagrangian functions publication-title: J. Optim. Theory Appl. doi: 10.1023/B:JOTA.0000012735.86699.a1 – volume: 183 start-page: 1 year: 2007 end-page: 19 ident: CR13 article-title: Approximate proximal methods in vector optimization publication-title: Eur. J. Oper. Res. doi: 10.1016/j.ejor.2006.09.070 – volume: 59 start-page: 63 year: 2010 end-page: 76 ident: CR49 article-title: One step from DC optimization to DC mixed variational inequalities publication-title: Optimization doi: 10.1080/02331930903500282 – volume: 93 start-page: 273 year: 1965 end-page: 299 ident: CR43 article-title: Proximité et dualité dans un espace Hilbertien publication-title: Bull. Soc. Math. Fr. doi: 10.24033/bsmf.1625 – volume: 23 start-page: 2169 year: 2013 end-page: 2182 ident: CR3 article-title: A subgradient method for vector optimization problems publication-title: SIAM J. Optim. doi: 10.1137/120866415 – volume: 28 start-page: 1104 issue: 2 year: 2018 end-page: 1120 ident: CR4 article-title: The proximal point method for locally Lipschitz functions in multiobjective optimization with application to the compromise problem publication-title: SIAM J. Optim. doi: 10.1137/16M107534X – volume: 108 start-page: 571 year: 2001 end-page: 586 ident: CR23 article-title: Simplified optimality conditions for minimizing the difference of vector-valued functions publication-title: J. Optim. Theory Appl. doi: 10.1023/A:1017535424813 – volume: 69 start-page: 297 year: 2018 end-page: 324 ident: CR67 article-title: A proximal difference-of-convex algorithm with extrapolation publication-title: Comput. Optim. Appl. doi: 10.1007/s10589-017-9954-1 – volume: 256 start-page: 17 year: 2017 end-page: 23 ident: CR11 article-title: A relaxed projection method for solving multiobjective optimization problems publication-title: Eur. J. Oper. Res. doi: 10.1016/j.ejor.2016.05.026 – volume: 2 start-page: 379 year: 2018 end-page: 389 ident: CR39 article-title: Optimality conditions for weakly efficient solutions of vector variational inequalities via convexificators publication-title: J. Nonlinear Var. Anal. – year: 1990 ident: CR17 publication-title: Optimization and Nonsmooth Analysis. Classics in Applied Mathematics doi: 10.1137/1.9781611971309 – ident: CR55 – ident: CR59 – ident: CR62 – volume: 4 start-page: 154 year: 1970 end-page: 159 ident: CR40 article-title: Regularisation d’inéquations variationelles par approximations succesives publication-title: Rev. Francaise d’Inform. Recherche Oper. – ident: 139_CR58 – volume: 214 start-page: 485 year: 2011 ident: 139_CR66 publication-title: Eur. J. Oper. Res. doi: 10.1016/j.ejor.2011.05.006 – volume: 12 start-page: 257 year: 2011 ident: 139_CR15 publication-title: J. Nonlinear Convex Anal. – volume: 183 start-page: 1 year: 2007 ident: 139_CR13 publication-title: Eur. J. Oper. Res. doi: 10.1016/j.ejor.2006.09.070 – volume: 19 start-page: 397 year: 2008 ident: 139_CR45 publication-title: SIAM J. Optim. doi: 10.1137/060655183 – volume: 20 start-page: 602 issue: 2 year: 2009 ident: 139_CR22 publication-title: SIAM J. Optim. doi: 10.1137/08071692X – volume: 14 start-page: 877 year: 1976 ident: 139_CR53 publication-title: SIAM J. Control. Optim. doi: 10.1137/0314056 – volume: 48 start-page: 183 year: 2010 ident: 139_CR20 publication-title: Glob. Optim. doi: 10.1007/s10898-009-9486-z – volume-title: Variational Analysis and Generalized Differentiation. I. Basic Theory, Grundlehren der Mathematischen Wissenschaften year: 2006 ident: 139_CR46 doi: 10.1007/3-540-31247-1 – volume: 235 start-page: 494 year: 2014 ident: 139_CR6 publication-title: Eur. J. Oper. Res. doi: 10.1016/j.ejor.2014.01.002 – volume: 15 start-page: 953 year: 2005 ident: 139_CR10 publication-title: SIAM J. Optim. doi: 10.1137/S1052623403429093 – volume: 4 start-page: 154 year: 1970 ident: 139_CR40 publication-title: Rev. Francaise d’Inform. Recherche Oper. – volume: 87 start-page: 13 year: 2005 ident: 139_CR9 publication-title: Ann. Polon. Math. doi: 10.4064/ap87-0-2 – ident: 139_CR59 – volume: 22 start-page: 557 year: 2014 ident: 139_CR5 publication-title: Set-Valued Var. Anal. doi: 10.1007/s11228-014-0279-2 – volume: 146 start-page: 267 year: 2010 ident: 139_CR14 publication-title: J. Optim. Theory Appl. doi: 10.1007/s10957-010-9667-4 – ident: 139_CR55 – volume-title: Variational Analysis and Applications year: 2018 ident: 139_CR48 doi: 10.1007/978-3-319-92775-6 – volume: 34 start-page: 585 year: 2014 ident: 139_CR25 publication-title: Pesqui. Oper. doi: 10.1590/0101-7438.2014.034.03.0585 – volume: 28 start-page: 1104 issue: 2 year: 2018 ident: 139_CR4 publication-title: SIAM J. Optim. doi: 10.1137/16M107534X – volume: 162 start-page: 821 year: 2014 ident: 139_CR28 publication-title: J. Optim. Theory Appl. doi: 10.1007/s10957-013-0327-3 – volume: 23 start-page: 107 year: 1998 ident: 139_CR37 publication-title: Acta Math. Vietnam – volume-title: Field Theory in Social Science. Harper Torchbooks year: 1964 ident: 139_CR36 – volume: 166 start-page: 172 year: 2015 ident: 139_CR7 publication-title: J. Optim. Theory Appl. doi: 10.1007/s10957-015-0711-2 – volume: 64 start-page: 79 year: 2016 ident: 139_CR1 publication-title: J. Glob. Optim. doi: 10.1007/s10898-015-0367-3 – volume: 28 start-page: 5 year: 2004 ident: 139_CR26 publication-title: Comput. Optim. Appl. doi: 10.1023/B:COAP.0000018877.86161.8b – volume-title: Handbook of Organizational Change and Innovation year: 2004 ident: 139_CR50 doi: 10.1093/oso/9780195135008.001.0001 – volume-title: Nonlinear Multiobjective Optimization year: 1999 ident: 139_CR41 – volume: 85 start-page: 157 year: 1999 ident: 139_CR31 publication-title: Math. Program. doi: 10.1007/s101070050050 – volume: 8 start-page: 476 year: 1998 ident: 139_CR63 publication-title: SIAM J. Optim. doi: 10.1137/S1052623494274313 – volume: 9 start-page: 707 year: 1959 ident: 139_CR29 publication-title: Pac. J. Math. doi: 10.2140/pjm.1959.9.707 – volume-title: Theory of Vector Optimization. Lecture Notes in Economics and Mathematical Systems year: 1989 ident: 139_CR38 – volume: 1 start-page: 5 year: 1947 ident: 139_CR35 publication-title: Hum. Relat. doi: 10.1177/001872674700100103 – volume: 69 start-page: 297 year: 2018 ident: 139_CR67 publication-title: Comput. Optim. Appl. doi: 10.1007/s10589-017-9954-1 – volume: 2 start-page: 379 year: 2018 ident: 139_CR39 publication-title: J. Nonlinear Var. Anal. – volume: 63 start-page: 797 year: 2015 ident: 139_CR60 publication-title: J. Glob. Optim. doi: 10.1007/s10898-015-0282-7 – ident: 139_CR56 – volume: 166 start-page: 199 year: 1992 ident: 139_CR12 publication-title: J. Math. Anal. Appl. doi: 10.1016/0022-247X(92)90336-C – volume: 59 start-page: 63 year: 2010 ident: 139_CR49 publication-title: Optimization doi: 10.1080/02331930903500282 – volume: 23 start-page: 501 year: 2015 ident: 139_CR8 publication-title: Set-Valued Var. Anal. doi: 10.1007/s11228-015-0319-6 – volume: 21 start-page: 451 year: 2003 ident: 139_CR61 publication-title: J. Comput. Math. – volume: 86 start-page: 319 year: 1982 ident: 139_CR64 publication-title: J. Math. Anal. Appl. doi: 10.1016/0022-247X(82)90226-8 – volume: 120 start-page: 111 year: 2004 ident: 139_CR32 publication-title: J. Optim. Theory Appl. doi: 10.1023/B:JOTA.0000012735.86699.a1 – volume: 23 start-page: 2169 year: 2013 ident: 139_CR3 publication-title: SIAM J. Optim. doi: 10.1137/120866415 – volume: 205 start-page: 247 year: 1975 ident: 139_CR16 publication-title: Trans. Am. Math. Soc. doi: 10.1090/S0002-9947-1975-0367131-6 – volume: 256 start-page: 37 year: 1986 ident: 139_CR30 publication-title: Convex. Dual. Optim. Lect. Notes Econ. Math. Syst. doi: 10.1007/978-3-642-45610-7_3 – ident: 139_CR18 doi: 10.1007/s10479-018-3104-8 – volume: 41 start-page: 451 year: 1983 ident: 139_CR42 publication-title: J. Optim. Theory Appl. doi: 10.1007/BF00935364 – ident: 139_CR62 doi: 10.1016/S0304-0208(08)72402-2 – volume: 61 start-page: 71 year: 2015 ident: 139_CR21 publication-title: J. Glob. Optim. doi: 10.1007/s10898-014-0159-1 – volume: 108 start-page: 571 year: 2001 ident: 139_CR23 publication-title: J. Optim. Theory Appl. doi: 10.1023/A:1017535424813 – volume: 4 start-page: 307 year: 1980 ident: 139_CR54 publication-title: Eur. J. Oper. Res. doi: 10.1016/0377-2217(80)90142-3 – volume: 235 start-page: 503 year: 2014 ident: 139_CR51 publication-title: Eur. J. Oper. Res. doi: 10.1016/j.ejor.2014.01.022 – volume: 256 start-page: 17 year: 2017 ident: 139_CR11 publication-title: Eur. J. Oper. Res. doi: 10.1016/j.ejor.2016.05.026 – volume: 247 start-page: 359 year: 2015 ident: 139_CR52 publication-title: Eur. J. Oper. Res. doi: 10.1016/j.ejor.2015.06.016 – ident: 139_CR57 – volume: 60 start-page: 961 year: 2011 ident: 139_CR2 publication-title: Optimization doi: 10.1080/02331931003770411 – volume: 54 start-page: 461 year: 2013 ident: 139_CR19 publication-title: Comput. Optim. Appl. doi: 10.1007/s10589-012-9494-7 – volume: 93 start-page: 273 year: 1965 ident: 139_CR43 publication-title: Bull. Soc. Math. Fr. doi: 10.24033/bsmf.1625 – volume: 41 start-page: 161 year: 1988 ident: 139_CR65 publication-title: Math. Program. doi: 10.1007/BF01580762 – volume: 175 start-page: 395 year: 2005 ident: 139_CR27 publication-title: J. Comput. Appl. Math. doi: 10.1016/j.cam.2004.06.018 – volume-title: Vector Optimization: Theory, Applications and Extensions year: 2004 ident: 139_CR33 doi: 10.1007/978-3-540-24828-6 – volume: 169 start-page: 280 year: 2016 ident: 139_CR34 publication-title: J. Optim. Theory Appl. doi: 10.1007/s10957-015-0847-0 – volume: 60 start-page: 1009 year: 2011 ident: 139_CR24 publication-title: Optimization doi: 10.1080/02331934.2010.522710 – volume-title: Optimization and Nonsmooth Analysis. Classics in Applied Mathematics year: 1990 ident: 139_CR17 doi: 10.1137/1.9781611971309 – volume: 61 start-page: 1383 year: 2012 ident: 139_CR44 publication-title: Optimization doi: 10.1080/02331934.2011.564623 – volume-title: Variational Analysis and Generalized Differentiation. II. Applications, Grundlehren der Mathematischen Wissenschaften year: 2006 ident: 139_CR47 doi: 10.1007/3-540-31246-3
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Snippet	We consider the constrained multi-objective optimization problem of finding Pareto critical points of difference of convex functions. The new approach proposed...
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SubjectTerms	Ascent Convex analysis Convex and Discrete Geometry Critical point Economics and Finance Goal programming Group dynamics Humanities and Social Sciences Iterative methods Management Science Mathematical analysis Mathematics Mathematics and Statistics Multiple objective analysis Operations Research Operations Research/Decision Theory Optimization Pareto optimization Statistics
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Title	A proximal point method for difference of convex functions in multi-objective optimization with application to group dynamic problems
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