Two seminars in optimization, one after the other, are taking place next Tuesday.
Speaker1: Fabian Flores-Bazan (University of Concepcion) Title1: Strong duality in nonconvex optimization with a single equality and geometric constraints: applications to QP Time1: Tuesday, June 30; 15:00 Place1: Sala seminari est, informatica
Speaker2: Marco Locatelli (Università di Parma) Title2: Some results about convex envelopes Time2: Tuesday, June 30; 15:45 Place2: Sala seminari est, informatica
Abstract1: The validity of strong duality for a non convex optimization problem under a single equality and geometric constraints is characterized in a topological and geometric manner. In particular, a hidden convexity of the conic hull of joint-range of the pair of functions associated to the original problem, is obtained. Applications to derive KKT conditions without standard constraints qualification are also discussed. Several examples showing our results provide much more information than those appearing elsewhere, are given. Furthermore, first and second order optimality condition, for a non convex quadratic optimization problem under two quadratic equality constraints, are also presented. Finally, the standard quadratic problem involving a non necessarily polyhedral cone is analyzed in detail.
The talk is based on joints works with G. Carcamo and F. Opazo.
Abstract2: In this talk we discuss convex envelopes for some bivariate functions over general polytopes and for some $n$-dimensional quadratic functions over the unit simplex. We first give two formulations of convex envelope, a primal and a dual one. Next, we discuss how to derive the convex envelope for some bivariate functions over polytopes, provided that some given assumptions are fulfilled. It will turn out that the formula of the convex envelope can be derived through the solution of a parametric convex program or, equivalently, through the solution of the corresponding KKT system. For what concerns the $n$-dimensional quadratic functions over the unit simplex, we will first associate a graph to the quadratic function, and next we will show that the derivation of the convex envelope is related to the identification of the spanning forests over this graph.
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Everyone is welcome!
On 23/06/15 09:42, Federico Poloni wrote:
Two seminars in optimization, one after the other, are taking place next Tuesday.
Speaker1: Fabian Flores-Bazan (University of Concepcion) Title1: Strong duality in nonconvex optimization with a single equality and geometric constraints: applications to QP Time1: Tuesday, June 30; 15:00 Place1: Sala seminari est, informatica
Speaker2: Marco Locatelli (Università di Parma) Title2: Some results about convex envelopes Time2: Tuesday, June 30; 15:45 Place2: Sala seminari est, informatica
Abstract1: The validity of strong duality for a non convex optimization problem under a single equality and geometric constraints is characterized in a topological and geometric manner. In particular, a hidden convexity of the conic hull of joint-range of the pair of functions associated to the original problem, is obtained. Applications to derive KKT conditions without standard constraints qualification are also discussed. Several examples showing our results provide much more information than those appearing elsewhere, are given. Furthermore, first and second order optimality condition, for a non convex quadratic optimization problem under two quadratic equality constraints, are also presented. Finally, the standard quadratic problem involving a non necessarily polyhedral cone is analyzed in detail.
The talk is based on joints works with G. Carcamo and F. Opazo.
Abstract2: In this talk we discuss convex envelopes for some bivariate functions over general polytopes and for some $n$-dimensional quadratic functions over the unit simplex. We first give two formulations of convex envelope, a primal and a dual one. Next, we discuss how to derive the convex envelope for some bivariate functions over polytopes, provided that some given assumptions are fulfilled. It will turn out that the formula of the convex envelope can be derived through the solution of a parametric convex program or, equivalently, through the solution of the corresponding KKT system. For what concerns the $n$-dimensional quadratic functions over the unit simplex, we will first associate a graph to the quadratic function, and next we will show that the derivation of the convex envelope is related to the identification of the spanning forests over this graph.
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Everyone is welcome!
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Federico Poloni -
Federico Poloni