Aussel, D., Correa, R., Marechal, M. (2011) Gap Functions for quasivariational Inequalities and Generalized Nash Equilibrium Problem, Journal of Optimization Theory and Applications, pp 474-488
Abstract
The gap function (or merit function) is a classic tool for reformulating a Stampacchia variational inequality as
an optimization problem. In this paper, we adapt this technique for quasivariational inequalities, that is, variational inequalities
in which the constraint set depends on the current point. Following Fukushima (J. Ind. Manag. Optim. 3:165-171, 2007), an axiomatic
approach is proposed. Error bounds for quasivariational inequalities are provided and an application to generalized Nash equilibrium
problems is also considered.
Aussel, D., Correa, R., Marechal, M. (2013) Spot Electricity Market with Transmission Losses, Journal of Industrial and Management Optimization, 2013, vol. 9, no 2, pp 275-290
Abstract
In order to study deregulated electricity spot markets, various
models have been proposed. Most of them correspond to a, so-called, multi-
leader-follower game in which an Independent System Operator (ISO) plays
a central role. Our aim in this paper is to consider quadratic bid functions
together with the transmission losses in the multi-leader-follower game. Under
some reasonable assumptions we deduce qualitative properties for the ISO's
problem. In the two islands type market, the explicit formulae for the optimal
solutions of the ISO's problem are obtained and we show the existence of an
equilibrium.
Aussel, D., Cervinka, M., Marechal, M., Correa, R. (2015) Deregulated Electricity Markets with Thermal Losses and Production Bounds: models and optimality conditions, Rairo-Operations Research, vol. 50, no 1, pp 19-38
Abstract
In this paper, we study the calmness of a generalized Nash equilibrium problem (GNEP) with non-differentiable data.
The approach consists in obtaining some error bound property for the KKT system associated with the generalized Nash equilibrium problem,
and returning to the primal problem thanks to the Slater constraint qualification.
Marechal, M., Correa, R. (2016) Error bounds, metric subregularity and stability in Generalized Nash Equilibrium Problems with nonsmooth payoff functions, Optimization, vol. 65, no 10, pp 1829-1854
Abstract
In this paper, we study the calmness of a generalized Nash equilibrium problem (GNEP) with non-differentiable data.
The approach consists in obtaining some error bound property for the KKT system associated with the generalized Nash equilibrium problem,
and returning to the primal problem thanks to the Slater constraint qualification.
Alvarez, F., Marechal, M., Correa, R. (2017) Regular Self-Proximal Distances are Bregman, Journal of Convex Analysis, vol. 24, no 1, pp 135-148
Abstract
Bregman distances play a key role in generalized versions of the proximal algorithm. This paper proposes a new characterization of Bregman distances in terms of their gradient and Hessian matrix.
Thanks to this characterization, we obtain two results: all the so called self-proximal distances are Bregman,
and all the induced proximal distances, under some regularity assumptions, are Bregman functions.
Marechal, M. (2018) Metric Subregularity in Generalized Equations, Journal of Optimization Theory and Application, Vol. 176, no 3, pp 541–558
Abstract
In this article, we study the metric subregularity of generalized equations using a new tool of nonsmooth analysis. We obtain a sufficient condition for a generalized equation to be metrically subregular,
which is not a necessary condition for metric regularity, using a subtle adjustment of the Mordukhovich coderivative. We apply these results to the study of the metric subregularity in a Cournot duopoly game.