A penalty function method for solving inverse optimal value problem

Authors:
Yibing Lv;Tiesong Hu;Zhongping Wan
Affiliations:
State Key Lab of Water Resource and Hydropower Engineering Science, Institute of Systems Engineering, Wuhan University, Wuhan 430072, PR China;State Key Lab of Water Resource and Hydropower Engineering Science, Institute of Systems Engineering, Wuhan University, Wuhan 430072, PR China;School of Mathematics and Statistics, Wuhan University, Wuhan 430072, PR China
Venue:
Journal of Computational and Applied Mathematics
Year:
2008

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Abstract

In order to consider the inverse optimal value problem under more general conditions, we transform the inverse optimal value problem into a corresponding nonlinear bilevel programming problem equivalently. Using the Kuhn-Tucker optimality condition of the lower level problem, we transform the nonlinear bilevel programming into a normal nonlinear programming. The complementary and slackness condition of the lower level problem is appended to the upper level objective with a penalty. Then we give via an exact penalty method an existence theorem of solutions and propose an algorithm for the inverse optimal value problem, also analysis the convergence of the proposed algorithm. The numerical result shows that the algorithm can solve a wider class of inverse optimal value problem.