Epigraphical polyhedral mappings with applications to multi-objective optimization

J. Parra López, M. J. Cánovas Cánovas, M. A. López Cerdá, B. Mordukhovich

We are concerned with (finite) linear inequality systems in Rⁿ parameterized by their right hand side. Roughly speaking, our focus is on measuring the variation of the feasible set around a given feasible point and in some given directions. This idea is formalized by means of the so-called epigraphical mapping obtained by adding to each feasible set a fixed (and polyhedral) cone. Such epigraphical sets are described as feasible sets of new linear inequality systems. As an application to ordinary linear programming, we describe a procedure to compute the optimal value function under right-hand side perturbations, and relate the Lipschitz modulus of this optimal value function with the Lipschitz modulus of an appropriate epigraphical mapping. The counterpart of this application for multiobjective optimization is also analyzed.

Keywords: Epigraphical set-valued mapping, feasible set mapping, Lipschitz modulus, linear programming, optimal value function, multi-objective programming

GT11-4 MA-4 Continuous Optimization. Tribute to Marco Antonio López
September 6, 2019  11:20 AM
I2L7. Georgina Blanes building

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