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Méthodes de réalisation de produit scalaire et de problème de moments avec maximisation d'entropie

Valerie Girardin (1997)

Studia Mathematica

We develop several methods of realization of scalar product and generalized moment problems. Constructions are made by use of a Hilbertian method or a fixed point method. The constructed solutions are rational fractions and exponentials of polynomials. They are connected to entropy maximization. We give the general form of the maximizing solution. We show how it is deduced from the maximizing solution of the algebraic moment problem.

Minimax control of nonlinear evolution equations

Nikolaos S. Papageorgiou (1995)

Commentationes Mathematicae Universitatis Carolinae

In this paper we study the minimax control of systems governed by a nonlinear evolution inclusion of the subdifferential type. Using some continuity and lower semicontinuity results for the solution map and the cost functional respectively, we are able to establish the existence of an optimal control. The abstract results are then applied to obstacle problems, semilinear systems with weakly varying coefficients (e.gȯscillating coefficients) and differential variational inequalities.

Minimax optimal control problems. Numerical analysis of the finite horizon case

Silvia C. Di Marco, Roberto L.V. González (2010)

ESAIM: Mathematical Modelling and Numerical Analysis

In this paper we consider the numerical computation of the optimal cost function associated to the problem that consists in finding the minimum of the maximum of a scalar functional on a trajectory. We present an approximation method for the numerical solution which employs both discretization on time and on spatial variables. In this way, we obtain a fully discrete problem that has unique solution. We give an optimal estimate for the error between the approximated solution and the optimal cost function...

Minimax theorems with applications to convex metric spaces

Jürgen Kindler (1995)

Colloquium Mathematicae

A minimax theorem is proved which contains a recent result of Pinelis and a version of the classical minimax theorem of Ky Fan as special cases. Some applications to the theory of convex metric spaces (farthest points, rendez-vous value) are presented.

Minimax theorems without changeless proportion

Liang-Ju Chu, Chi-Nan Tsai (2003)

Discussiones Mathematicae, Differential Inclusions, Control and Optimization

The so-called minimax theorem means that if X and Y are two sets, and f and g are two real-valued functions defined on X×Y, then under some conditions the following inequality holds: i n f y ∈ Y s u p x ∈ X f ( x , y ) ≤ s u p x ∈ X i n f y ∈ Y g ( x , y ) . We will extend the two functions version of minimax theorems without the usual condition: f ≤ g. We replace it by a milder condition: s u p x ∈ X f ( x , y ) ≤ s u p x ∈ X g ( x , y ) , ∀y ∈ Y. However, we require some restrictions; such as, the functions f and g are jointly upward, and their upper sets are connected. On the other hand, by using some properties...

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