Abstract variational problems with volume constraints

Optimal Control of Problems Governed by Abstract Elliptic Variational Inequalities with State Constraints∗

In this paper we investigate optimal control problems governed by elliptic variational inequalities with additional state constraints. We present a relaxed formulation for the problem. With penalization methods and approximation techniques we give qualification conditions to get first-order optimality conditions.

Homogenization of Variational Problems under Manifold Constraints

Abstract. Homogenization of integral functionals is studied under the constraint that admissible maps have to take their values into a given smooth manifold. The notion of tangential homogenization is defined by analogy with the tangential quasiconvexity introduced by Dacorogna, Fonseca, Malý & Trivisa [18]. For energies with superlinear or linear growth, a Γ-convergence result is established i...

Handling Convexity-Like Constraints in Variational Problems

We provide a general framework to construct finite-dimensional approximations of the space of convex functions, which also applies to the space of c-convex functions and to the space of support functions of convex bodies. We give precise estimates of the distance between the approximation space and the admissible set. This framework applies to the approximation of convex functions by piecewise-...

Duality for vector equilibrium problems with constraints

‎In the paper‎, ‎we study duality for vector equilibrium problems using a concept of generalized convexity in dealing with the quasi-relative interior‎. ‎Then‎, ‎their applications to optimality conditions for quasi-relative efficient solutions are obtained‎. ‎Our results are extensions of several existing ones in the literature when the ordering cones in both the objective space and the constr...

Sensitivity Analysis for Optimization Problems with Variational Inequality Constraints