Sequential optimality conditions for cardinality-constrained optimization problems with applications

Optimality Conditions for Constrained Optimization Problems

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...

On sequential optimality conditions for smooth constrained optimization

Sequential optimality conditions provide adequate theoretical tools to justify stopping criteria for nonlinear programming solvers. Approximate KKT and Approximate Gradient Projection conditions are analyzed in this work. These conditions are not necessarily equivalent. Implications between different conditions and counter-examples will be shown. Algorithmic consequences will be discussed.

Optimality Conditions for Constrained Optimization

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...