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A Piecewise Convexification Method for Solving Bilevel Programs with A Nonconvex Follower's Problem

Gaoxi Li(ligaoxicn***at***126.com)

Abstract: A new numerical method is presented for bilevel programs with a nonconvex follower's problem. The basic idea is to piecewise construct convex relations of the follower's problem, replace the relaxed follower's problem equivalently by their Karush-Kuhn-Tucker conditions, and solve the resulting mathematical programs with equilibrium constraints. The convex relaxations and needed parameters are constructed with ideas of the $\alpha BB$ method of global optimization. Under mild conditions, we prove that every accumulated point of the solutions of the sequence approximate problems is an optimal solution of the original problem, and the convergence theorem of this algorithm is presented and proved. Numerical experiments show that the algorithm is efficient for solving this class of bilevel programs.

Keywords: Bilevel programs, Equilibrium constraints, Global optimization, Piecewise convexification

Category 1: Complementarity and Variational Inequalities

Citation: 1 School of Mathematics and Statistics, Chongqing Technology and Business University 1/2018

Download: [PDF]

Entry Submitted: 12/23/2018
Entry Accepted: 12/30/2018
Entry Last Modified: 12/23/2018

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