On Bilevel Programs with a Convex Lower-Level Problem Violating Slater’s Constraint Qualification

Gaoxi Li () and Zhongping Wan ()
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Gaoxi Li: Chongqing Technology and Business University
Zhongping Wan: Wuhan University

Journal of Optimization Theory and Applications, 2018, vol. 179, issue 3, No 5, 820-837

Abstract: Abstract This paper focuses on bilevel programs with a convex lower-level problem violating Slater’s constraint qualification. We relax the constrained domain of the lower-level problem. Then, an approximate solution of the original bilevel program can be obtained by solving this perturbed bilevel program. As the lower-level problem of the perturbed bilevel program satisfies Slater’s constraint qualification, it can be reformulated as a mathematical program with complementarity constraints which can be solved by standard algorithms. The lower convergence properties of the constraint set mapping and the solution set mapping of the lower-level problem of the perturbed bilevel program are expanded. We show that the solutions of a sequence of the perturbed bilevel programs are convergent to that of the original bilevel program under some appropriate conditions. And this convergence result is applied to simple trilevel programs.

Keywords: Nonlinear programs; Bilevel programs; Slater’s constraint qualification; Complementarity constraints; Lower convergence; 90C33; 90C30 (search for similar items in EconPapers)
Date: 2018
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Citations: View citations in EconPapers (1)

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DOI: 10.1007/s10957-018-1392-4

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