On parametric vector optimization via metric regularity of constraint systems

Some metric and graphical regularity properties of generalized constraint systems are investigated. Then, these properties are applied in order to penalize (in the sense of Clarke) various scalar and vector optimization problems. This method allows us to present several necessary optimality conditions in solid constrained vector optimization.

[1]  Marius Durea,et al.  On some Fermat rules for set-valued optimization problems , 2011 .

[2]  R. Rockafellar,et al.  Implicit Functions and Solution Mappings , 2009 .

[3]  Kok Lay Teo,et al.  Sharp Minima for Multiobjective Optimization in Banach Spaces , 2006 .

[4]  S. J. Li,et al.  Weak -Sharp Minima in Vector Optimization Problems , 2010 .

[5]  Stephen M. Robinson,et al.  Strongly Regular Generalized Equations , 1980, Math. Oper. Res..

[6]  F. Clarke.  Optimization And Nonsmooth Analysis , 1983 .

[7]  Marius Durea,et al.  Openness stability and implicit multifunction theorems: Applications to variational systems , 2011, 1102.0415.

[8]  Boris S. Mordukhovich,et al.  Subgradient of distance functions with applications to Lipschitzian stability , 2005, Math. Program..

[9]  X. Q. Yang,et al.  Weak sharp minima for set-valued vector variational inequalities with an application , 2010, Eur. J. Oper. Res..

[10]  L. Thibault.  On subdifferential of optimal value functions , 1991 .

[11]  X. Q. Yang,et al.  Weak Sharp Minima in Multicriteria Linear Programming , 2005, SIAM J. Optim..

[12]  Jen-Chih Yao,et al.  CODERIVATIVES OF EFFICIENT POINT MULTIFUNCTIONS IN PARAMETRIC VECTOR OPTIMIZATION , 2009 .

[13]  Jane J. Ye,et al.  Partial Exact Penalty for Mathematical Programs with Equilibrium Constraints , 2008 .

[14]  Xiaoqi Yang,et al.  Weak sharp minima for piecewise linear multiobjective optimization in normed spaces , 2008 .

[15]  Sien Deng,et al.  Weak sharp minima revisited, part II: application to linear regularity and error bounds , 2005, Math. Program..

[16]  R. Rockafellar,et al.  Lipschitzian properties of multifunctions , 1985 .

[17]  Boris S. Mordukhovich,et al.  Multiobjective optimization problems with equilibrium constraints , 2008, Math. Program..

[18]  Christiane Tammer,et al.  Fuzzy necessary optimality conditions for vector optimization problems , 2009 .

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

[20]  A. Göpfert.  Variational methods in partially ordered spaces , 2003 .

[21]  Bao Truong.  Necessary conditions for multiobjective optimization with preferences , 2009 .

[22]  Boris S. Mordukhovich,et al.  Necessary Conditions in Multiobjective Optimization with Equilibrium Constraints , 2007 .