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Nash equilibrium for a multiobjective control problem related to wastewater management

Néstor García-Chan, Rafael Muñoz-Sola, Miguel Ernesto Vázquez-Méndez (2009)

ESAIM: Control, Optimisation and Calculus of Variations

This paper is concerned with mathematical modelling in the management of a wastewater treatment system. The problem is formulated as looking for a Nash equilibrium of a multiobjective pointwise control problem of a parabolic equation. Existence of solution is proved and a first order optimality system is obtained. Moreover, a numerical method to solve this system is detailed and numerical results are shown in a realistic situation posed in the estuary of Vigo (Spain).


Nash equilibrium payoffs for stochastic differential games with reflection

Qian Lin (2013)

ESAIM: Control, Optimisation and Calculus of Variations

In this paper, we investigate Nash equilibrium payoffs for nonzero-sum stochastic differential games with reflection. We obtain an existence theorem and a characterization theorem of Nash equilibrium payoffs for nonzero-sum stochastic differential games with nonlinear cost functionals defined by doubly controlled reflected backward stochastic differential equations.

Nonconcentrating generalized Young functionals

Tomáš Roubíček (1997)

Commentationes Mathematicae Universitatis Carolinae

The Young measures, used widely for relaxation of various optimization problems, can be naturally understood as certain functionals on suitable space of integrands, which allows readily various generalizations. The paper is focused on such functionals which can be attained by sequences whose “energy” (= p th power) does not concentrate in the sense that it is relatively weakly compact in L 1 ( Ω ) . Straightforward applications to coercive optimization problems are briefly outlined.

Nonconvex Duality and Semicontinuous Proximal Solutions of HJB Equation in Optimal Control

Mustapha Serhani, Nadia Raïssi (2009)

RAIRO - Operations Research

In this work, we study an optimal control problem dealing with differential inclusion. Without requiring Lipschitz condition of the set valued map, it is very hard to look for a solution of the control problem. Our aim is to find estimations of the minimal value, (α), of the cost function of the control problem. For this, we construct an intermediary dual problem leading to a weak duality result, and then, thanks to additional assumptions of monotonicity of proximal subdifferential, we give a more...

Notes on free lunch in the limit and pricing by conjugate duality theory

Alena Henclová (2006)

Kybernetika

King and Korf [KingKorf01] introduced, in the framework of a discrete- time dynamic market model on a general probability space, a new concept of arbitrage called free lunch in the limit which is slightly weaker than the common free lunch. The definition was motivated by the attempt at proposing the pricing theory based on the theory of conjugate duality in optimization. We show that this concept of arbitrage fails to have a basic property of other common concepts used in pricing theory – it depends...

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