Speaker: Fabián Flores Bazán Affiliation: Departamento de Ingeniería Matemática, Universidad de Concepción, Chile Time and date: Monday, 4th July 2016, 15:00 Place: Sala Seminari Est, Dipartimento di Informatica, Università di Pisa

Title: A semi-infinite programming approach for the circular conic StQOP: strong duality, optimality and hidden convexity

Abstract: Many formulations of quadratic allocation problems, portfolio optimization problems, the maximum weight clique problem, among others, take the form as the well-known standard quadratic optimization problem, which consist in minimizing a homogeneous quadratic function on the usual simplex in the non negative orthant. We propose to analyze the same problem when the simplex is substituted by a convex and compact base of any pointed, closed, convex (possibly circular) cone. It is associated three main duals (for which a semi-infinite formulation of the primal problem is required) and establish some characterizations of strong duality with respect to each of the three duals in terms of copositivity of the Hessian of the quadratic objective function on suitable cones. Such a problem reveals a hidden convexity.

Part of the results were obtained jointly with G. Cárcamo and S. Caro. This research is supported in part by CONICYT-Chile through FONDECYT 115-0973 and BASAL projects, CMM, Universidad de Chile.

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