Strong stability in nonlinear programming revisited

Abstract The paper revisits characterizations of strong stability and strong regularity of KarushKuhn-Tucker solutions of nonlinear programs with twice differentiable data. We give a unified framework to handle both concepts simultaneously.

[1]  Jiming Liu Strong Stability in Variational Inequalities , 1995 .

[2]  H. Gfrerer Hölder continuity of solutions of perturbed optimization problems under Mangasarian-Fromovitz constraint qualification , 1987 .

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

[4]  Jan-J. Rückmann,et al.  On inertia and schur complement in optimization , 1987 .

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

[6]  B. Kummer,et al.  Stability Properties of Infima and Optimal Solutions of Parametric Optimization Problems , 1985 .

[7]  D. Klatte,et al.  Strong stability of stationary solutions and Karush-Kuhn-Tucker points in nonlinear optimization , 1991 .

[8]  Bernd Kummer An Implicit- Function Theorem for Co*' -Equations and Parametric Cl*' -Optimization , 1991 .

[9]  Lionel Thibault,et al.  On generalized differentials and subdifferentials of Lipschitz vector-valued functions , 1982 .

[10]  Hubertus Th. Jongen,et al.  On Iterated Minimization in Nonconvex Optimization , 1986, Math. Oper. Res..

[11]  D. Du,et al.  Recent Advances in Nonsmooth Optimization , 1995 .

[12]  Diethard Klatte,et al.  Generalized Kojima–Functions and Lipschitz Stability of Critical Points , 1999, Comput. Optim. Appl..

[13]  Stephen M. Robinson,et al.  Normal Maps Induced by Linear Transformations , 1992, Math. Oper. Res..

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

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

[16]  Stephan Dempe,et al.  Directional derivatives of the solution of a parametric nonlinear program , 1995, Math. Program..

[17]  R. Rockafellar,et al.  Characterizations of Lipschitzian Stability in Nonlinear Programming , 2020 .

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

[19]  Hubertus Th. Jongen,et al.  Implicit functions and sensitivity of stationary points , 1990, Math. Program..

[20]  Daniel Ralph,et al.  Sensitivity analysis of composite piecewise smooth equations , 1997, Math. Program..

[21]  F. Clarke,et al.  Topological Geometry: THE INVERSE FUNCTION THEOREM , 1981 .

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

[23]  Jong-Shi Pang,et al.  Piecewise Smoothness, Local Invertibility, and Parametric Analysis of Normal Maps , 1996, Math. Oper. Res..

[24]  Alexander Shapiro,et al.  Optimization Problems with Perturbations: A Guided Tour , 1998, SIAM Rev..

[25]  B. Kummer The Inverse of a Lipschitz Function in Rn: Complete Characterization by Directional Derivates , 1989 .

[26]  Related Topics,et al.  Parametric Optimization and Related Topics V , 1987 .

[27]  J. Frédéric Bonnans,et al.  Pseudopower expansion of solutions of generalized equations and constrained optimization problems , 1995, Math. Program..

[28]  Jong-Shi Pang Necessary and Sufficient Conditions for Solution Stability of Parametric Nonsmooth Equations , 1995 .

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

[30]  Diethard Pallaschke,et al.  Nondifferentiable Optimization: Motivations and Applications , 1985 .

[31]  R. Tyrrell Rockafellar,et al.  Sensitivity analysis for nonsmooth generalized equations , 1992, Math. Program..

[32]  Adam B. Levy,et al.  Sensitivity of Solutions in Nonlinear Programming Problems with Nonunique Multipliers , 1995 .

[33]  BonnansJ. Frédéric,et al.  Optimization Problems with Perturbations , 1998 .

[34]  R. Tyrrell Rockafellar,et al.  Characterizations of Strong Regularity for Variational Inequalities over Polyhedral Convex Sets , 1996, SIAM J. Optim..

[35]  Bernd Kummer An implicit-function theorem for C0, 1-equations and parametric C1, 1-optimization , 1991 .

[36]  Adam B. Levy,et al.  Implicit multifunction theorems for the sensitivity analysis of variational conditions , 1996, Math. Program..

[37]  B. Kummer Lipschitzian inverse functions, directional derivatives, and applications inC1,1 optimization , 1991 .