Infinite Optimization Problem Research Articles

On the approximation of infinite optimization problems with an application to optimal control problems

This paper is concerned with approximations to infinite optimization problems in Banach spaces. Under the assumption of a first order necessary and a second order sufficient optimality condition we derive convergence results for the optimal solutions and the optimal values of the approximating problems. An application to finite difference approximations of nonlinear optimal control problems with state constraints is given.

Continuity properties in semi-infinite parametric linear optimization

In this paper, we treat optimization problems of the following type: minimize a linear functional p on a closed, convex subset of Euclidean m-space. (Semi- infinite linear optimization problems are of this type.) We investigate upper semicontinuity of the set of optimal solutions and the continuous dependence of the optimal value on p. Thereby we essentially work with the concept of characteristic cones of closed, convex sets.

Continuous perturbations of infinite optimization problems

In this paper, continuity properties of the extremal value function and the solution function are studied for general optimization problems with perturbations in the objective function and the constraints. A classical stability condition is extended and compared with constraint qualification conditions.