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Deterministic upper bounds in global minimization with nonlinear equality constraints

Christian Füllner (christian.fuellner***at***kit.edu)
Peter Kirst (peter-kirst***at***web.de)
Oliver Stein (stein***at***kit.edu)

Abstract: We address the problem of deterministically determining upper bounds in continuous non-convex global minimization of box-constrained problems with equality constraints. These upper bounds are important for the termination of spatial branch-and-bound algorithms. Our method is based on the theorem of Miranda which helps to ensure the existence of feasible points in certain boxes. Then, the computation of upper bounds at the objective function over those boxes yields an upper bound for the globally minimal value. A proof of convergence is given under mild assumptions. An extension of our approach to problems including inequality constraints is possible.

Keywords: Branch-and-bound; deterministic upper bounds; feasibility verification; theorem of Miranda

Category 1: Global Optimization (Theory )

Category 2: Nonlinear Optimization (Constrained Nonlinear Optimization )

Citation: Optimization Online, Preprint ID 2018-11-6913, 2018.

Download: [PDF]

Entry Submitted: 11/06/2018
Entry Accepted: 11/06/2018
Entry Last Modified: 11/06/2018

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