Optimal control for a class of mechanical thermoviscoelastic frictional contact problems
Optimal control for elasto-orthotropic plate
Optimal control in coefficients for elliptic variational inequalities and optimality conditions
Optimal control in some variational inequalities
Optimal control of a frictionless contact problem with normal compliance
We consider a mathematical model which describes a contact between an elastic body and a foundation. The contact is frictionless with normal compliance. The goal of this paper is to study an optimal control problem which consists of leading the stress tensor as close as possible to a given target, by acting with a control on the boundary of the body. We state an optimal control problem which admits at least one solution. Next, we establish an optimality condition corresponding to a regularization...
Optimal control of a variational inequality with possibly nonsymmetric linear operator. Application to the obstacle problems in mathematical physics.
Optimal control of obstacle problems : existence of Lagrange multipliers
Optimal Control of Obstacle Problems: Existence of Lagrange Multipliers
We study first order optimality systems for the control of a system governed by a variational inequality and deal with Lagrange multipliers: is it possible to associate to each pointwise constraint a multiplier to get a “good” optimality system? We give positive and negative answers for the finite and infinite dimensional cases. These results are compared with the previous ones got by penalization or differentiation.
Optimal control of problems governed by obstacle type variational inequalities: A dual regularization-penalization approach.
Optimal control problems for variational inequalities with controls in coefficients and in unilateral constraints
We deal with an optimal control problem for variational inequalities, where the monotone operators as well as the convex sets of possible states depend on the control parameter. The existence theorem for the optimal control will be applied to the optimal design problems for an elasto-plastic beam and an elastic plate, where a variable thickness appears as a control variable.
Optimal design of cylindrical shell with a rigid obstacle
The aim of the present paper is to study problems of optimal design in mechanics, whose variational form are inequalities expressing the principle of virtual power in its inequality form. We consider an optimal control problem in whixh the state of the system (involving an elliptic, linear symmetric operator, the coefficients of which are chosen as the design - control variables) is defined as the (unique) solution of stationary variational inequalities. The existence result proved in Section 1...
Optimal design of laminated plate with obstacle
The aim of the present paper is to study problems of optimal design in mechanics, whose variational form is given by inequalities expressing the principle of virtual power in its inequality form. The elliptic, linear symmetric operators as well as convex sets of possible states depend on the control parameter. The existence theorem for the optimal control is applied to design problems for an elastic laminated plate whose variable thickness appears as a control variable.
Optimal design problems for a dynamic viscoelastic plate. I. Short memory material
We deal with an optimal control problem with respect to a variable thickness for a dynamic viscoelastic plate with velocity constraints. The state problem has the form of a pseudohyperbolic variational inequality. The existence and uniqueness theorem for the state problem and the existence of an optimal thickness function are proved.
Optimal Regularity Theorems for Variational Problems with Obstacles.
Optimal solutions for a model of tumor anti-angiogenesis with a penalty on the cost of treatment
The scheduling of angiogenic inhibitors to control a vascularized tumor is analyzed as an optimal control problem for a mathematical model that was developed and biologically validated by Hahnfeldt et al. [Cancer Res. 59 (1999)]. Two formulations of the problem are considered. In the first one the primary tumor volume is minimized for a given amount of angiogenic inhibitors to be administered, while a balance between tumor reduction and the total amount of angiogenic inhibitors given is minimized...
Optimal stopping and impulsive control of one-dimensional diffusion processes
Optimality conditions for nonconvex variational problems relaxed in terms of Young measures
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.
Painlevé-Kuratowski convergences for the solution sets of set-valued weak vector variational inequalities.
Parametric general variational-like inequality problem in uniformly smooth Banach space.
Parametric monotone generalized equations in reflexive Banach spaces.