Optimality Conditions for Irregular Inequality-Constrained Problems

Optimality Conditions for Irregular Inequality-Constrained Problems

We consider feasible sets given by conic constraints, where the cone defining the constraints is convex with nonempty interior. We study the case where the feasible set is not assumed to be regular in the classical sense of Robinson and obtain a constructive description of the tangent cone under a certain new second-order regularity condition. This condition contains classical regularity as a s...

Optimality Conditions for Constrained Optimization Problems

Necessary Optimality Conditions for Optimization Problems with Variational Inequality Constraints

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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...

Optimality Conditions for Constrained Optimization