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Solving disjunctive optimization problems by generalized semi-infinite optimization techniques

Peter Kirst (kirst***at***kit.edu)
Oliver Stein (stein***at***kit.edu)

Abstract: We describe a new possibility to model disjunctive optimization problems as generalized semi-infinite programs. In contrast to existing methods, for our approach neither a conjunctive nor a disjunctive normal form is expected. Applying existing lower level reformulations for the corresponding semi-infinite program we derive conjunctive nonlinear problems without any logical expressions, which can be locally solved by standard nonlinear solvers. Our preliminary numerical results on some small-scale examples indicate that our reformulation procedure is a reasonable method to solve disjunctive optimization problems.

Keywords: Disjunctive optimization, generalized semi-infinite optimization, lower level duality, mathematical program with complementarity constraints, smoothing.

Category 1: Infinite Dimensional Optimization (Semi-infinite Programming )

Category 2: Convex and Nonsmooth Optimization (Nonsmooth Optimization )

Citation: Journal of Optimization Theory and Applications, 2016, DOI 10.1007/s10957-016-0862-9

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Entry Submitted: 02/27/2015
Entry Accepted: 02/27/2015
Entry Last Modified: 01/18/2016

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