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Indexed by:Journal Papers

Date of Publication:2015-10-01

Journal:PACIFIC JOURNAL OF OPTIMIZATION

Included Journals:SCIE

Volume:11

Issue:4,SI

Page Number:687-703

ISSN No.:1348-9151

Key Words:inverse optimization; complementarity constraints; smoothing function

Abstract:This paper proposes a general inverse nonlinear optimization model in which parameters in both objective function and in constraints are required to be estimated. The inverse optimization model is reformulated as a mathematical programming problem with simple complementarity constraints. The tangent cone, normal cone of the feasible region of the inverse optimization problem are developed under mild conditions. First and second-order necessary optimality conditions as well as the second-order sufficient optimality conditions are derived. The smoothed Fischer-Burmeister function is used to construct a smoothing approach for solving the inverse nonlinear optimization problem. It is demonstrated that, when the positive smoothing parameter approaches to 0, the feasible set of the smoothing problem is convergent to the feasible set of the inverse problem, the global optimal value of the smoothing problem converges to that of the inverse problem, the outer limit of the solution mapping is contained in the solution set of the inverse problem, and the outer limit of the KKT-point mapping is contained in the set of Clarke stationary points associated with corresponding multipliers.