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On localizing global Pareto solutions in a given convex set

Agnieszka Drwalewska, Lesław Gajek (1999)

Applicationes Mathematicae

Sufficient conditions are given for the global Pareto solution of the multicriterial optimization problem to be in a given convex subset of the domain. In the case of maximizing real valued-functions, the conditions are sufficient and necessary without any convexity type assumptions imposed on the function. In the case of linearly scalarized vector-valued functions the conditions are sufficient and necessary provided that both the function is concave and the scalarization is increasing with respect...

On necessary optimality conditions in a class of optimization problems

Jiří V. Outrata (1989)

Aplikace matematiky

In the paper necessary optimality conditions are derived for the minimization of a locally Lipschitz objective with respect to the consttraints x ∈ S , 0 ∈ F ( x ) , where S is a closed set and F is a set-valued map. No convexity requirements are imposed on F . The conditions are applied to a generalized mathematical programming problem and to an abstract finite-dimensional optimal control problem.

On some general almost periodic optimal control problems : links with periodic problems and necessary conditions

Denis Pennequin (2008)

ESAIM: Control, Optimisation and Calculus of Variations

In this paper, we are concerned with periodic, quasi-periodic (q.p.) and almost periodic (a.p.) Optimal Control problems. After defining these problems and setting them in an abstract setting by using Abstract Harmonic Analysis, we give some structure results of the set of solutions, and study the relations between periodic and a.p. problems. We prove for instance that for an autonomous concave problem, the a.p. problem has a solution if and only if all problems (periodic with fixed or variable...

On some general almost periodic Optimal Control problems: links with periodic problems and necessary conditions

Denis Pennequin (2007)

ESAIM: Control, Optimisation and Calculus of Variations

In this paper, we are concerned with periodic, quasi-periodic (q.p.) and almost periodic (a.p.) Optimal Control problems. After defining these problems and setting them in an abstract setting by using Abstract Harmonic Analysis, we give some structure results of the set of solutions, and study the relations between periodic and a.p. problems. We prove for instance that for an autonomous concave problem, the a.p. problem has a solution if and only if all problems (periodic with fixed or variable...

On the characteristic properties of certain optimization problems in complex analysis

Józef Baranowicz, Leon Mikołajczyk (1995)

Banach Center Publications

We shall be concerned in this paper with an optimization problem of the form: J(f) → min(max) subject to f ∈ 𝓕 where 𝓕 is some family of complex functions that are analytic in the unit disc. For this problem, the question about its characteristic properties is considered. The possibilities of applications of the results of general optimization theory to such a problem are also examined.

Optimal control of ∞-dimensional stochastic systems via generalized solutions of HJB equations

N.U. Ahmed (2001)

Discussiones Mathematicae, Differential Inclusions, Control and Optimization

In this paper, we consider optimal feedback control for stochastc infinite dimensional systems. We present some new results on the solution of associated HJB equations in infinite dimensional Hilbert spaces. In the process, we have also developed some new mathematical tools involving distributions on Hilbert spaces which may have many other interesting applications in other fields. We conclude with an application to optimal stationary feedback control.

Optimal control of nonlinear evolution equations

Nikolaos S. Papageorgiou, Nikolaos Yannakakis (2001)

Discussiones Mathematicae, Differential Inclusions, Control and Optimization

In this paper, first we consider parametric control systems driven by nonlinear evolution equations defined on an evolution triple of spaces. The parametres are time-varying probability measures (Young measures) defined on a compact metric space. The appropriate optimization problem is a minimax control problem, in which the system analyst minimizes the maximum cost (risk). Under general hypotheses on the data we establish the existence of optimal controls. Then we pass to nonparametric...

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