Optimization and Equilibrium

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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On regularization/convexification of functionals including an l2-misfit term

Event Date: Mar 14, 2018 in Optimization and Equilibrium, Seminars

Abstract: A common technique for solving ill-posed inverse problems is to include some sparsity/low-rank constraint, and pose it as a convex optimization problem, as is done e.g. in compressive sensing. The corresponding functional to be minimized often includes an l2 data fidelity term plus a convex term forcing sparsity. However, for many applications a non-convex term would be more suitable, although this is usually discarded since it leads to issues with algorithm convergence, local minima etc. I will introduce a new transform to (partially) convexify non-convex functionals of the above...

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Projected solutions of quasi-variational inequalities with application to bidding process in electricity market

Event Date: Jan 17, 2018 in Optimization and Equilibrium, Seminars

Abstract:   Quasi-variational inequalities provide perfect tools  to reformulate Generalized Nash Equilibrium Probem (GNEP), the latter being a good model to describe the day-ahead  electricity markets.   Our aim in this talk is to illustrate how some recent advances in the theory  of quasi-variational inequalities can influence the modeling of electricity market.   Talk based on: – D. Aussel, A. Sultana & V. Vetrivel, On the existence of projected solutions of quasi-variational inequalities and generalized Nash equilibrium problem, J. Optim. Th. Appl. 170 (2016),...

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Projected solutions for quasi-equilibrium problems.

Event Date: Dec 06, 2017 in Optimization and Equilibrium, Seminars

Abstract:   In 2016, Aussel, Sultana and Vetrivel introduced the concept of projected solutions for generalized Nash equilibrium problems (GNEPs)in the finite dimensional case. To show the existence  of such solutions they studied projected solutions for quasi-variational inequality problems. In a similar spirit, we introduce the concept of projected solution for quasi-equilibrium problems (QEPs). As a consequence of our main result we obtain an existence result for projected solutions of GNEPs, in infinite dimensional spaces.  

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Existence results for equilibrium problem

Event Date: Nov 08, 2017 in Optimization and Equilibrium, Seminars

Abstract:   In this paper, we introduce certain regularizations for bifunctions, based on the corresponding regularization for functions, originally defined by J-P. Crouzeix. We show that the equilibrium problems associated to a bifunction and its regularizations are equivalent in the sense that they share the same solution set. Also, we introduce new existence results for the Equilibrium Problem, and we show some applications to minimization and Nash equilibrium...

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