Continuity of minimal points with applications to parametric multiple objective optimization

Abstract Basing ourselves on general results we investigate stability of Pareto points to finite-dimensional parametric multiple objective optimization problems (linear and/or convex).

[1]  Ewa M. Bednarczuk.  Some stability results for vector optimization problems in partially ordered topological vector spaces , 1996 .

[2]  R. Holmes.  Geometric Functional Analysis and Its Applications , 1975 .

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

[4]  S. Bolintinéanu,et al.  Second-Order Efficiency Conditions and Sensitivity of Efficient Points , 1998 .

[5]  J. Frédéric Bonnans,et al.  Perturbation Analysis of Optimization Problems , 2000, Springer Series in Operations Research.

[6]  E. Bednarczuk.  Hoelder-like properties of minimal points in vector optimization , 2002 .

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

[8]  A. Peressini.  Ordered topological vector spaces , 1967 .

[9]  B. Bank,et al.  Non-Linear Parametric Optimization , 1983 .

[10]  Adam B. Levy.  Scaled Stability in Variational Problems , 2002, SIAM J. Optim..

[11]  G. Y. Chen,et al.  Existence and continuity of solutions for vector optimization , 1994 .

[12]  ADAM B. LEVY,et al.  Solution Sensitivity from General Principles , 2001, SIAM J. Control. Optim..

[13]  Mordechai I. Henig.  The domination property in multicriteria optimization , 1986 .

[14]  Sien Deng.  Perturbation analysis of a condition number for convex inequality systems and global error bounds for analytic systems , 1998, Math. Program..

[15]  D. Azé,et al.  On the Sensitivity Analysis of Hoffman Constants for Systems of Linear Inequalities , 2002, SIAM J. Optim..

[16]  Tetsuzo Tanino,et al.  Stability and sensitivity analysis in multiobjective nonlinear programming , 1990 .

[17]  Martin Petschke.  On a theorem of Arrow, Barankin, and Blackwell , 1990 .

[18]  Alicia Sterna-Karwat.  Convexity of the optimal multifunctions and its consequences in vector optimization , 1989 .

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