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1

A method of lower and upper solutions for control problems and application to a model of bone marrow transplantation

Parajdi Lorand Gabriel, Precup Radu, Haplea Ioan Ştefan

International Journal of Applied Mathematics and Computer Science

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2023

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Vol. 33, no. 3

409--418

EN

A lower and upper solution method is introduced for control problems related to abstract operator equations. The method is illustrated on a control problem for the Lotka-Volterra model with seasonal harvesting and applied to a control problem of cell evolution after bone marrow transplantation.

2

On the multiobjective control problem

Kumar P., Sharma B.

Journal of Applied Analysis

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2018

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Vol. 24, nr 2

223--231

EN

In this paper, sufficient optimality conditions are established for the multiobjective control problem using efficiency of higher order as a criterion for optimality. The ρ-type 1 invex functionals (taken in pair) of higher order are proposed for the continuous case. Existence of such functionals is confirmed by a numer of examples. It is shown with the help of an example that this class is more general than the existing class of functionals.Weak and strong duality theorems are also derived for a mixed dual in order to relate efficient solutions of higher order for primal and dual problems.

3

Generalized α-V-univex functions for multiobjective variational control problems

Sharma S., Choudhury S., Jayswal A.

Control and Cybernetics

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2014

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Vol. 43, no. 3

403--420

EN

The purpose of this paper is to introduce a new class of _-V-univex/ generalized _-V-univex functions for a class of multiobjective variational control problems. Moreover, sufficient optimality conditions and Mond-Weir type duality results, associated with the multiobjective variational control problem, are established under aforesaid assumptions.

4

Optimal control for a class of mechanical thermoviscoelastic frictional contact problems

Denkowski Z., Migórski S., Ochal A.

Control and Cybernetics

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2007

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Vol. 36, no 3

611-632

EN

We study optimal control of systems governed by a coupled system of hemivariational inequalities, modeling a dynamic thermoviscoelastic problem, which describes frictional contact between a body and a foundation. We employ the Kelvin-Voigt vis-coelastic law, include the thermal effects and consider the general nonmonotone and multivalued subdifferential boundary conditions. We consider optimal control problem for boundary and distributed parameter control systems, time optimal control problem and maximum stay control problem. We deliver conditions that guarantee the existence of optimal solutions.

5

Sensitivity of optimal solutions to control problems for systems described by hemivariational inequalities

Denkowski Z., Migórski S.

Control and Cybernetics

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2004

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Vol. 33, no 2

211-236

EN

In this paper the sensitivity of optimal solutions to control problems for the systems described by stationary and evolution heinivariational inequalities (HVIs) under perturbations of state relations and of cost functionals is investigated. First, basing on the theory of sequential [Gamma]-convergence we recall the abstract scheme concerning convergence of minimal values and minimizers. The abstract scheme works provided we can establish two properties: the Kuratowski convergence of solution sets for HVIs (state relations) and some complementary [Gamma]-convergence of the cost functionals. Then these two properties are implemented in each considered case.