Generalized Minty vector variational-like inequalities and vector optimization problems in Asplund spaces

We consider two generalized Minty vector variational-like inequalities and investigate the relations between their solutions and vector optimization problems for non-differentiable α-invex functions.

[1]  B. Mond,et al.  Pre-invex functions in multiple objective optimization , 1988 .

[2]  Kok Lay Teo,et al.  Some Remarks on the Minty Vector Variational Inequality , 2004 .

[3]  Kok Lay Teo,et al.  Generalized Invexity and Generalized Invariant Monotonicity , 2003 .

[4]  Generalized Invariant Monotonicity and Generalized Invexity of Nondifferentiable Functions , 2009 .

[5]  Aris Daniilidis,et al.  Subdifferential characterization of approximate convexity: the lower semicontinuous case , 2008, Math. Program..

[6]  Xiaoqi Yang,et al.  Vector variational-like inequality with pseudoinvexity , 2006 .

[7]  F. Giannessi.  On Minty Variational Principle , 1998 .

[8]  Jen-Chih Yao,et al.  On generalized variational-like inequalities with generalized monotone multivalued mappings , 2009, Appl. Math. Lett..

[9]  Jafar Zafarani,et al.  Generalized Vector Variational-Like Inequalities , 2008 .

[10]  Zita Poracká-Diviš.  Existence Theorem and Convergence of Minimizing Sequences in Extremum Problems , 1971 .

[11]  Jafar Zafarani,et al.  Vector optimization and variational-like inequalities , 2009, J. Glob. Optim..

[12]  Ya-Ping Fang,et al.  A non-smooth version of Minty variational principle , 2009 .

[13]  M. Soleimani-damaneh.  Characterizations and applications of generalized invexity and monotonicity in Asplund spaces , 2012 .

[14]  Panos M. Pardalos,et al.  Handbook of Multicriteria Analysis , 2010 .

[15]  Bin Chen,et al.  Vector variational-like inequalities and vector optimization problems in Asplund spaces , 2012, Optim. Lett..

[16]  Qamrul Hasan Ansari,et al.  Nonsmooth Vector Optimization Problems and Minty Vector Variational Inequalities , 2010 .

[17]  M. Fakhar,et al.  Generalized Vector Equilibrium Problems for Pseudomonotone Multivalued Bifunctions1 , 2005 .

[18]  Jafar Zafarani,et al.  Vector optimization problem and generalized convexity , 2012, J. Glob. Optim..

[19]  Antonio Rufián-Lizana,et al.  Generalized invex monotonicity , 2003, Eur. J. Oper. Res..

[20]  Kok Lay Teo,et al.  Criteria for generalized invex monotonicities , 2005, Eur. J. Oper. Res..

[21]  Qamrul Hasan Ansari,et al.  Generalized vector variational-like inequalities and vector optimization , 2012, J. Glob. Optim..

[22]  Jafar Zafarani,et al.  Generalized Invariant Monotonicity and Invexity of Non-differentiable Functions , 2006, J. Glob. Optim..

[23]  B. Mordukhovich.  Variational analysis and generalized differentiation , 2006 .

[24]  Panos M. Pardalos,et al.  A survey of recent developments in multiobjective optimization , 2007, Ann. Oper. Res..

[25]  Jian-Wen Peng,et al.  Generalized vector variational-like inequalities and nonsmooth vector optimization problems , 2012 .

[26]  P. Pardalos,et al.  Pareto optimality, game theory and equilibria , 2008 .

[27]  S. Itoh,et al.  Variational inequalities and complementarity problems , 1978 .

[28]  Q. H. Ansari,et al.  Generalized Minty Vector Variational-Like Inequalities and Vector Optimization Problems , 2009 .

[29]  S. R. Mohan,et al.  On Invex Sets and Preinvex Functions , 1995 .

[30]  Bastian Goldlücke,et al.  Variational Analysis , 2014, Computer Vision, A Reference Guide.