Lipschitz-Type Stability in Nonsmooth Convex Programs

This paper deals with upper Lipschitzian continuity of the optimal solution to parametrized convex programs with linear equality and inequality constraints and with a convex nondifferentiable objective function. Under quadratic growth conditions for the objective function, some accurate bound for the rate of the upper Lipschitzian continuity is provided.

[1]  K. Jittorntrum.  Solution point differentiability without strict complementarity in nonlinear programming , 1984 .

[2]  S. M. Robinson.  Stability Theory for Systems of Inequalities, Part II: Differentiable Nonlinear Systems , 1976 .

[3]  Alexander Shapiro,et al.  Second order sensitivity analysis and asymptotic theory of parametrized nonlinear programs , 1985, Math. Program..

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

[5]  J. Gauvin,et al.  Directional Lipschitzian Optimal Solutions and Directional Derivative for the Optimal Value Function in Nonlinear Mathematical Programming , 1989 .

[6]  Alexander D. Ioe.  Quadratic Growth and Stability in Convex Programming Problems with Multiple Solutions , 1995 .

[7]  Alexander Shapiro,et al.  On Lipschitzian Stability of Optimal Solutions of Parametrized Semi-Infinite Programs , 1994, Math. Oper. Res..

[8]  A. Shapiro.  Sensitivity analysis of nonlinear programs and differentiability properties of metric projections , 1988 .

[9]  J. Hiriart-Urruty,et al.  Convex analysis and minimization algorithms , 1993 .

[10]  Jean-Pierre Aubin,et al.  Lipschitz Behavior of Solutions to Convex Minimization Problems , 1984, Math. Oper. Res..

[11]  Anthony V. Fiacco,et al.  Nonlinear programming;: Sequential unconstrained minimization techniques , 1968 .

[12]  Jacques Gauvin,et al.  Directional Behaviour of Optimal Solutions in Nonlinear Mathematical Programming , 1988, Math. Oper. Res..

[13]  William W. Hager,et al.  Implicit Functions, Lipschitz Maps, and Stability in Optimization , 1994, Math. Oper. Res..

[14]  Stephen M. Robinson,et al.  An Implicit-Function Theorem for a Class of Nonsmooth Functions , 1991, Math. Oper. Res..

[15]  A. Auslender,et al.  First and second order sensitivity analysis of nonlinear programs under directional constraint qualification conditions , 1990 .