A necessary and a sufficient optimality condition for bilevel programming problems

A necessary and a sufficient condition for local optimal solutions of bilevel programming problems are developed using differential stability results for parametric optimization problems. Verification of these conditions reduces to the solution of some auxiliary combinatorial optimization problems.

[1]  V. Klee.  SEPARATION AND SUPPORT PROPERTIES OF CONVEX SETS: A SURVEY. , 1969 .

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

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

[4]  José Fortuny-Amat,et al.  A Representation and Economic Interpretation of a Two-Level Programming Problem , 1981 .

[5]  Laurence A. Wolsey,et al.  An elementary survey of general duality theory in mathematical programming , 1981, Math. Program..

[6]  T. Başar,et al.  Dynamic Noncooperative Game Theory , 1982 .

[7]  Jonathan F. Bard,et al.  An explicit solution to the multi-level programming problem , 1982, Comput. Oper. Res..

[8]  Wilfred Candler,et al.  A linear two-level programming problem, , 1982, Comput. Oper. Res..

[9]  E. Aiyoshi,et al.  A solution method for the static constrained Stackelberg problem via penalty method , 1984 .

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

[11]  J. Bard.  Optimality conditions for the bilevel programming problem , 1984 .

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

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

[14]  M. Studniarski.  Necessary and sufficient conditions for isolated local minima of nonsmooth functions , 1986 .

[15]  J. Zowe,et al.  Approximation to a set-valued mapping, I: A proposal , 1986 .

[16]  J. Penot,et al.  A new constraint qualification condition , 1986 .

[17]  S. Dempe.  A simple algorithm for the-linear bilevel programming problem , 1987 .

[18]  R. Lucchetti,et al.  Existence theorems of equilibrium points in stackelberg , 1987 .

[19]  S. M. Robinson.  Local structure of feasible sets in nonlinear programming, Part III: Stability and sensitivity , 1987 .

[20]  Jonathan F. BARD,et al.  Convex two-level optimization , 1988, Math. Program..

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

[22]  J. Morgan,et al.  e-regularized two-level optimization problems: approximation and existence results , 1988 .

[23]  D. E. Ward.  Exact penalties and sufficient conditions for optimality in nonsmooth optimization , 1988 .

[24]  Stephan Dempe,et al.  On the directional derivative of the optimal solution mapping without linear independence constraint qualification , 1989 .

[25]  Jirí Vladimír Outrata,et al.  On the numerical solution of a class of Stackelberg problems , 1990, ZOR Methods Model. Oper. Res..

[26]  Stephan Dempe,et al.  Directional differentiability of optimal solutions under Slater's condition , 1993, Math. Program..