Noticias en español
Modeling energy markets with bilevel games
Abstract: Once upon a time, electricity was merely a fairy tale. Since it has been mastered and distributed though, ensuring the supply-demand balance has always been a challenge. Instead of constantly adapting the production to the demand, a new approach consisting in adapting the demand to the production arose about thirty years ago. This approach is called demand-side management, and can be applied through various techniques, notably pricing: offering time-dependent electricity prices can influence the demand. After a small introduction on bilevel programming, we consider a bilevel energy...
Read MoreFarkas’ lemma: some extensions and applications
Abstract: The classical Farkas’ lemma characterizing the linear inequalities which are consequence of an ordinary linear system was proved in 1902 by this Hungarian Physicist to justify the first order necessary optimality condition for nonlinear programming problems stated by Ostrogradski in 1838. At present, any result characterizing the containment of the solution set of a given system in the sublevel sets of a given function is said to be a Farkas-type lemma. These results provide partial answers to the so-called containment problem, consisting in characterizing the inclusion of a...
Read MoreHidden Convexity in the l0 Pseudonorm and Lower Bound Convex Programs for Exact Sparse Optimization
Abstract: In sparse optimization problems, one looks for solution that have few nonzero components. We consider problems where sparsity is exactly measured by the l0 pseudonorm. We display a suitable conjugacy for which we show that the l0 pseudonorm is equal to its biconjugate. As a corollary, we obtain that the (nonconvex) l0 pseudonorm coincides, on the sphere, with a convex lsc function that we characterize. With this conjugacy, we display a lower bound for the original exact sparse optimization problem, which is a convex minimization program over the unit ball of a...
Read MoreProgressive Decoupling of Linkages in Optimization with Elicitable Convexity
ABSTRACT: A method called the Progressive Decoupling Algorithm is described for solving variational inequalities and optimization problems in which a subspace captures “linkages” that can be relaxed. The approach is inspired by the Progressive Hedging Algorithm in convex stochastic programming and resembles the Partial Inverse Method of Spingarn, but retains more parametric flexibility than the latter. It is able even to work when mononicity or convexity is not directly present but can be “elicited”. The role of elicitation mimics the role of...
Read MoreAn approach to optimality in convex optimization via some new Moreau- Rockafellar type formulas for the subdifferential of the supremum function.
Abstract: We present different characterizations of the subdifferential of the supremum function of finitely and infinitely indexed families of convex functions under weak continuity assumptions. The resulting formulas are given in terms of the exact subdifferential of the data functions at the reference point, and not at nearby points. Based on these characterizations we give new Fritz-John and KKT-type optimality conditions for semi-infinite convex optimization, dropping out the typical continuity/closedness assumptions which are usual in the literature. The presentation is a selection of...
Read More“Second-order characterizations of C1-smooth robustly quasiconvex functions”
Abstract: “Our aim in this talk is to investigate the possibility of using the Fréchet and Mordukhovich second-order subdifferentials to characterize the robust quasiconvexity of C1-smooth functions. We set up a necessary condition for the robust quasiconvexity of C1,1-smooth functions and univariate C1-smooth ones. We also show that the established necessary condition is indeed a sufficient one for the robust quasiconvexity of C1-smooth functions.”
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