Optimality Conditions for Convex Stochastic Optimization Problems in Banach Spaces with Almost Sure State Constraints

Optimality Conditions for Disjunctive Optimization in Reflexive Banach Spaces

Descent methods for convex optimization problems in Banach spaces

where f : E→ R is a convex function; see, for example, [1, 2, 8] and the references therein. It is well known that standard iterative methods for solving (1.2), which are designed for finite-dimensional optimization problems, cannot guarantee strong convergence of their iteration sequences to a solution of the initial problem if the cost function does not possess strengthened convexity properti...

Global Optimality Conditions for Quadratic Optimization Problems with Binary Constraints

We consider nonconvex quadratic optimization problems with binary constraints. Our main result identifies a class of quadratic problems for which a given feasible point is global optimal. We also establish a necessary global optimality condition. These conditions are expressed in a simple way in terms of the problem’s data. We also study the relations between optimal solutions of the nonconvex ...

Necessary Optimality Conditions for Optimization Problems with Variational Inequality Constraints

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Optimality Conditions for Optimization Problems with Complementarity Constraints

Optimization problems with complementarity constraints are closely related to optimization problems with variational inequality constraints and bilevel programming problems. In this paper, under mild constraint qualifications, we derive some necessary and sufficient optimality conditions involving the proximal coderivatives. As an illustration of applications, the result is applied to the bilev...