Branch-and-Sandwich: a deterministic global optimization algorithm for optimistic bilevel programming problems. Part II: Convergence analysis and numerical results

Polyxeni-M. Kleniati and Claire Adjiman ()

Journal of Global Optimization, 2014, vol. 60, issue 3, 459-481

Abstract: In the first part of this work, we presented a global optimization algorithm, Branch-and-Sandwich, for optimistic bilevel programming problems that satisfy a regularity condition in the inner problem (Kleniati and Adjiman in J Glob Optim, 2014 ). The proposed approach can be interpreted as the exploration of two solution spaces (corresponding to the inner and the outer problems) using a single branch-and-bound tree, where two pairs of lower and upper bounds are computed: one for the outer optimal objective value and the other for the inner value function. In the present paper, the theoretical properties of the proposed algorithm are investigated and finite $$\varepsilon $$ ε -convergence to a global solution of the bilevel problem is proved. Thirty-four problems from the literature are tackled successfully. Copyright The Author(s) 2014

Keywords: Bilevel programming; Nonconvex inner problem; Branch and bound (search for similar items in EconPapers)
Date: 2014
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Citations: View citations in EconPapers (12)

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DOI: 10.1007/s10898-013-0120-8

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