Existence and Optimality Conditions for Risk-Averse PDE-Constrained Optimization

Optimality Conditions for Constrained Optimization

Optimality Conditions for Constrained Optimization Problems

Optimality Conditions and Complexity for Non-Lipschitz Constrained Optimization Problems

In this paper, we consider a class of nonsmooth, nonconvex constrained optimization problems where the objective function may be not Lipschitz continuous and the feasible set is a general closed convex set. Using the theory of the generalized directional derivative and the Clarke tangent cone, we derive a first order necessary optimality condition for local minimizers of the problem, and define...

Strict Constraint Qualifications and Sequential Optimality Conditions for Constrained Optimization

Sequential optimality conditions for constrained optimization are necessarily satisfied by local minimizers, independently of the fulfillment of constraint qualifications. These conditions support the employment of different stopping criteria for practical optimization algorithms. On the other hand, when an appropriate strict constraint qualification associated with some sequential optimality c...

Algorithms for PDE-Constrained Optimization

In this paper we review a number of algorithmic approaches for solving optimization problems with PDE constraints. Most of these methods were originally developed for finite dimensional problems. When applied to optimization problems with PDE constraints, new aspects become important. For instance, (discretized) PDE-constrained problems are inherently large-scale. Some aspects, like mesh indepe...