Deterministic upper bounds for spatial branch-and-bound methods in global minimization with nonconvex constraints

Peter Kirst (), Oliver Stein () and Paul Steuermann ()

TOP: An Official Journal of the Spanish Society of Statistics and Operations Research, 2015, vol. 23, issue 2, 616 pages

Abstract: We discuss some difficulties in determining valid upper bounds in spatial branch-and-bound methods for global minimization in the presence of nonconvex constraints. In fact, two examples illustrate that standard techniques for the construction of upper bounds may fail in this setting. Instead, we propose to perturb infeasible iterates along Mangasarian–Fromovitz directions to feasible points whose objective function values serve as upper bounds. These directions may be calculated by the solution of a single linear optimization problem per iteration. Preliminary numerical results indicate that our enhanced algorithm solves optimization problems where a standard branch-and-bound method does not converge to the correct optimal value. Copyright Sociedad de Estadística e Investigación Operativa 2015

Keywords: Branch-and-bound; Convergence; Consistency; Mangasarian–Fromovitz constraint qualification; 90C26 (search for similar items in EconPapers)
Date: 2015
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Citations: View citations in EconPapers (8)

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DOI: 10.1007/s11750-015-0387-7

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