Stability of Stationary Solutions in Semi-Infinite Optimization via the Reduction Approach

The purpose of the paper is to characterize local minimizers of semi-infinite optimization problems as stable or strongly stable stationary solutions when a parameter appears in the objective function. By using the reduction approach, a special parametric nonsmooth optimization problem comes into consideration. We present stability results for this nonsmooth program and apply them to the initial problem.

[1]  W. Wetterling,et al.  Definitheitsbedingungen für relative Extrema bei Optimierungs- und Approximationsaufgaben , 1970 .

[2]  Marc Teboulle,et al.  Second order necessary optimality conditions for semi-infinite programming problems , 1979 .

[3]  Hubertus Th. Jongen,et al.  Semi-infinite optimization: Structure and stability of the feasible set , 1990 .

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

[5]  Hidefumi Kawasaki Second order necessary optimality conditions for minimizing a sup-type function , 1991, Math. Program..

[6]  Alexander Shapiro,et al.  Second-Order Derivatives of Extremal-Value Functions and Optimality Conditions for Semi-Infinite Programs , 1985, Math. Oper. Res..

[7]  B. Kummer NEWTON's METHOD FOR NON-DIFFERENTIABLE FUNCTIONS , 1988, Advances in Mathematical Optimization.

[8]  Georg J. Still,et al.  Semi-infinite programming models in robotics , 1991 .

[9]  Rainer Hettich,et al.  Numerische Methoden der Approximation und semi-infiniten Optimierung , 1982 .

[10]  D. Klatte,et al.  On second-order sufficient optimality conditions for c 1,1-optimization problems , 1988 .

[11]  H. Th. Jongen,et al.  On sufficient conditions for local optimality in semi-infinite programming , 1987 .

[12]  A. Ioffe Variational analysis of a composite function: A formula for the lower second order epi-derivative☆ , 1991 .

[13]  R. Rockafellar First- and second-order epi-differentiability in nonlinear programming , 1988 .

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

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

[16]  Asen L. Dontchev,et al.  On the regularity of the Kuhn-Tucker curve , 1986 .

[17]  R. W. Chaney Optimality conditions for piecewiseC2 nonlinear programming , 1989 .

[18]  Kenneth O. Kortanek,et al.  Semi-Infinite Programming and Applications , 1983, ISMP.

[19]  A. D. Ioffe Second Order Conditions in Nonlinear Nonsmooth Problems of Semi-Infinite Programming , 1983 .

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

[21]  J. Hiriart-Urruty,et al.  Generalized Hessian matrix and second-order optimality conditions for problems withC1,1 data , 1984 .

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

[23]  Diethard Klatte,et al.  On Procedures for Analysing Parametric Optimization Problems , 1982 .

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

[26]  D. Klatte Nonlinear Optimization Problems under Data Perturbations , 1992 .

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