Sensitivity Analysis for Nonlinear Programs and Variational Inequalities with Nonunique Multipliers

We extend the principal sensitivity analysis results for parametric nonlinear programs and variational inequalities by considering problems with nonunique optimal Lagrange multipliers. Specifically, we derive sufficient conditions for the existence, continuity and directional differentiability of a locally unique perturbed solution of a nonlinear program or a variational inequality.

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

[2]  A. Fiacco,et al.  Sensitivity analysis in nonlinear programming under second order assumptions , 1985 .

[3]  K. Jittorntrum.  Sequential algorithms in nonlinear programming , 1978, Bulletin of the Australian Mathematical Society.

[4]  R. Janin.  Directional derivative of the marginal function in nonlinear programming , 1984 .

[5]  A. Bagchi,et al.  Systems and Optimization , 1985 .

[6]  S. M. Robinson.  Implicit B-Differentiability in Generalized Equations. , 1985 .

[7]  Anthony V. Fiacco,et al.  Sensitivity analysis for nonlinear programming using penalty methods , 1976, Math. Program..

[8]  Jerzy Kyparisis,et al.  On uniqueness of Kuhn-Tucker multipliers in nonlinear programming , 1985, Math. Program..

[9]  Jerzy Kyparisis,et al.  Sensitivity analysis framework for variational inequalities , 1987, Math. Program..

[10]  Stephen M. Robinson,et al.  Perturbed Kuhn-Tucker points and rates of convergence for a class of nonlinear-programming algorithms , 1974, Math. Program..

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

[12]  Thomas L. Magnanti,et al.  Sensitivity Analysis for Variational Inequalities Defined on Polyhedral Sets , 1989, Math. Oper. Res..

[13]  S. M. Robinson.  Generalized equations and their solutions, part II: Applications to nonlinear programming , 1982 .

[14]  Jacques Gauvin,et al.  A necessary and sufficient regularity condition to have bounded multipliers in nonconvex programming , 1977, Math. Program..

[15]  J. Kyparisis.  Perturbed solutions of variational inequality problems over polyhedral sets , 1988 .

[16]  S. M. Robinson.  Analysis and computation of fixed points , 1980 .

[17]  M. Kojima.  Strongly Stable Stationary Solutions in Nonlinear Programs. , 1980 .

[18]  Stella Dafermos,et al.  Sensitivity Analysis in Variational Inequalities , 1988, Math. Oper. Res..

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

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

[21]  Jerzy Kyparisis.  Sensitivity analysis for non-linear programs with linear constraints , 1987 .

[22]  R. Tobin.  Sensitivity analysis for variational inequalities , 1986 .

[23]  Alfonso Reinoza.  The Strong Positivity Conditions , 1985, Math. Oper. Res..