Colloquium Mathematics - Prof. dr. S.M. Grad University of Vienna

Title: Employing Proximal Point Methods for Solving Nonlinear Minmax Location Problems via Conjugate Duality

Abstract:

The nonlinear minmax location problems are organic generalizations of the classical Sylvester problem (that consists in finding the smallest circle that encloses finitely many given points), and in general are difficult to handle because of their complicate structure. Motivation to study such optimization problems comes also from fields like Economics (e.g. production facility placement), Logistics (e.g. distribution facility placement), Urban Development (e.g. placement of public utilities and services), or Product Design (optimal components placement). We investigate via a conjugate duality approach general nonlinear minmax location problems, delivering necessary and sufficient optimality conditions together with characterizations of their optimal solutions in some particular instances. A parallel splitting proximal point method is employed for numerically solving such problems and their duals. We present computational results obtained in Matlab on concrete examples consisting in finding the disc or sphere with minimal radius that intersects some given sets, comparing these, where possible, with recent similar ones from the literature.

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