Sensitivity analysis for a Lagrange dual problem to a vector optimization problem

In this paper, sensitivity analysis for a Lagrange dual problem to a vector optimization problem is firstly studied. Then sensitivity analysis of the vector optimization problem is also discussed. Finally, the dual relationships between the obtained results are established.

[1]  S. J. Li,et al.  Second-Order Differential and Sensitivity Properties of Weak Vector Variational Inequalities , 2009 .

[2]  Shengjie Li,et al.  Differential and sensitivity properties of gap functions for Minty vector variational inequalities , 2008 .

[3]  S. J. Li,et al.  Conjugate dual problems in constrained set-valued optimization and applications , 2009, Eur. J. Oper. Res..

[4]  Hong Yan,et al.  Differential and sensitivity properties of gap functions for vector variational inequalities , 2003, Math. Methods Oper. Res..

[5]  Y. Sawaragi,et al.  Duality theory in multiobjective programming , 1979 .

[6]  T. Tanino,et al.  Sensitivity analysis in multiobjective optimization , 1988 .

[7]  R. Weiner.  Lecture Notes in Economics and Mathematical Systems , 1985 .

[8]  J. Aubin.  Set-valued analysis , 1990 .

[9]  Xiaoqi Yang,et al.  Duality in optimization and variational inequalities , 2002 .

[10]  S. J. Li,et al.  Robinson metric regularity of parametric variational systems , 2011 .

[11]  Tetsuzo Tanino,et al.  Stability and Sensitivity Analysis in Convex Vector Optimization , 1988 .

[12]  C. Tammer,et al.  Theory of Vector Optimization , 2003 .

[13]  Sorin-Mihai Grad,et al.  Duality for set-valued optimization problems based on vector conjugacy , 2009 .

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

[15]  D. Shi,et al.  Sensitivity analysis in convex vector optimization , 1993 .

[16]  Hirotaka Nakayama,et al.  Theory of Multiobjective Optimization , 1985 .

[17]  J. Aubin,et al.  Applied Nonlinear Analysis , 1984 .

[18]  Tetsuzo Tanino,et al.  Sensitivity analysis in vector optimization , 1996 .

[19]  Sorin-Mihai Grad,et al.  Duality in Vector Optimization , 2009, Vector Optimization.

[20]  Tetsuzo Tanino,et al.  Conjugate Duality in Vector Optimization , 1992 .

[21]  Radu Ioan Bot,et al.  Duality and optimality in multiobjective optimization , 2003 .

[22]  Shengjie Li,et al.  Sensitivity analysis of parametric weak vector equilibrium problems , 2011 .

[23]  R. Rockafellar.  Proto-Differentiability of Set-Valued Mappings and its Applications in Optimization☆ , 1989 .

[24]  R. Boţ,et al.  Conjugate duality in vector optimization and some applications to the vector variational inequality , 2007 .

[25]  H. Nakayama,et al.  Geometric consideration of duality in vector optimization , 1984 .

[26]  Zhongfei Li,et al.  ε-Conjugate maps and ε-conjugate duality in vector optimization with set-valued maps , 2008 .

[27]  D. Shi,et al.  Contingent derivative of the perturbation map in multiobjective optimization , 1991 .