Convexification Method for Bilevel Programs with a Nonconvex Follower’s Problem

Gaoxi Li () and Xinmin Yang ()
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Gaoxi Li: Chongqing Technology and Business University
Xinmin Yang: Chongqing Normal University

Journal of Optimization Theory and Applications, 2021, vol. 188, issue 3, No 6, 724-743

Abstract: Abstract A new numerical method is presented for bilevel programs with a nonconvex follower’s problem. The basic idea is to piecewise construct convex relaxations of the follower’s problems, replace the relaxed follower’s problems 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 piecewise convexity method of global optimization. Under mild conditions, we show that every accumulation point of the optimal solutions of the sequence approximate problems is an optimal solution of the original problem. The convergence theorems of this method are presented and proved. Numerical experiments show that this method is capable of solving this class of bilevel programs.

Keywords: Bilevel program; Equilibrium constraint; Global optimization; Piecewise convexification; 90C26; 90C30; 90C33 (search for similar items in EconPapers)
Date: 2021
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DOI: 10.1007/s10957-020-01804-9

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