Optimization and Equilibrium

Progressive Decoupling of Linkages in Optimization with Elicitable Convexity

Event Date: Mar 13, 2019 in Optimization and Equilibrium, Seminars

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...

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An approach to optimality in convex optimization via some new Moreau- Rockafellar type formulas for the subdifferential of the supremum function.

Event Date: Nov 07, 2018 in Optimization and Equilibrium, Seminars

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...

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“Second-order characterizations of C1-smooth robustly quasiconvex functions”

Event Date: Oct 24, 2018 in Optimization and Equilibrium, Seminars

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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A Study of the Difference-of-Convex Approach for Solving Linear Programs with Complementarity Constraints

Event Date: Sep 05, 2018 in Optimization and Equilibrium, Seminars

Abstract:   This work studies the difference-of-convex (DC) penalty formulations and the associated difference-of-convex algorithm (DCA) for computing stationary solutions of linear programs with complementarity constraints (LPCCs). We focus on two such formulations and establish connections between their stationary solutions and those of the LPCC. Improvements of the DCA are proposed to remedy some drawbacks in a straightforward adaptation of the DCA to these formulations. Extensive numerical results, including comparisons with an existing nonlinear programming solver and the...

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Convergence of projection algorithms: some results and counterexamples.

Event Date: May 30, 2018 in Optimization and Equilibrium, Seminars

Abstract:   Projection methods can be used for solving a range of feasibility and optimisation problems. Whenever the constraints are represented as the intersection of closed (convex) sets with readily implementable projections onto each of these sets, a projection based algorithm can be employed to force the iterates towards the feasible set. Some versions of projection methods employ approximate projections; one can also consider under- and over-relaxed iterations (such as in the Douglas-Rachford method). In this talk I will focus on the convergence of projection methods. This...

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A Game Theoretic Model for Optimizing Electricity Consumers Flexibilities in the Smart Grid.

Event Date: May 16, 2018 in Optimization and Equilibrium, Seminars

Abstract: With the evolution of electricity usages (electric vehicles, smart appliances) and the development of communication structures (smart grid), new opportunities of optimization have emerged for the actors of the electrical network. Aggregators can send signals to enrolled consumers to play on their demand flexibilities, and to optimize the providing costs and the social welfare. Game theory has been shown to be a valuable tool to study strategic electricity consumers participating in such a demand side management program. We propose a simple billing mechanism where the aggregator...

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