2000 Mathematics Subject Classification: Primary 90C29; Secondary 49K30.In this paper, we establish necessary optimality conditions and sufficient optimality conditions for D.C. vector optimization problems under D.C. constraints. Under additional conditions, some results of [9] and [15] are also recovered.
The scalar nonconvex variational problems of the minimum-energy type on Sobolev spaces are studied. As the Euler–Lagrange equation dramatically looses selectivity when extended in terms of the Young measures, the correct optimality conditions are sought by means of the convex compactification theory. It turns out that these conditions basically combine one part from the Euler–Lagrange equation with one part from the Weierstrass condition.
An optimal control problem for semilinear parabolic partial differential equations is considered. The control variable appears in the leading term of the equation. Necessary conditions for optimal controls are established by the method of homogenizing spike variation. Results for problems with state constraints are also stated.
An optimal control problem for semilinear parabolic partial differential equations is considered. The control variable appears in the leading term of the equation. Necessary conditions for optimal controls are established by the method of homogenizing spike variation. Results for problems with state constraints are also stated.
We consider a convex optimization problem with a vector valued function as objective function and convex cone inequality constraints. We suppose that each entry of the objective function is the composition of some convex functions. Our aim is to provide necessary and sufficient conditions for the weakly efficient solutions of this vector problem. Moreover, a multiobjective dual treatment is given and weak and strong duality assertions are proved.
The paper develops an approach to optimal design problems based on application of abstract optimisation principles in the space of measures. Various design criteria and constraints, such as bounded density, fixed barycentre, fixed variance, etc. are treated in a unified manner providing a universal variant of the Kiefer-Wolfowitz theorem and giving a full spectrum of optimality criteria for particular cases. Incorporating the optimal design problems into conventional optimisation framework makes...
The paper develops an approach to optimal design problems based on application of abstract optimisation principles in the space of measures. Various design criteria and constraints, such as bounded density, fixed barycentre, fixed variance, etc. are treated in a unified manner providing a universal variant of the Kiefer-Wolfowitz theorem and giving a full spectrum of optimality criteria for particular cases. Incorporating the optimal design problems into conventional optimisation framework...
The chronotherapy concept takes advantage of the circadian rhythm of cells physiology in maximising a treatment efficacy on its target while minimising its toxicity on healthy organs. The object of the present paper is to investigate mathematically and numerically optimal strategies in cancer chronotherapy. To this end a mathematical model describing the time evolution of efficiency and toxicity of an oxaliplatin anti-tumour treatment has been derived. We then applied an optimal control technique...
The chronotherapy concept takes advantage of the circadian rhythm of cells physiology in maximising a treatment efficacy on its target while minimising its toxicity on healthy organs. The object of the present paper is to investigate mathematically and numerically optimal strategies in cancer chronotherapy. To this end a mathematical model describing the time evolution of efficiency and toxicity of an oxaliplatin anti-tumour treatment has been derived. We then applied an optimal control...
In this paper we consider the optimal control of both operators and parameters for uncertain systems. For the optimal control and identification problem, we show existence of an optimal solution and present necessary conditions of optimality.