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We obtain a formula for the modulus of metric regularity of a mapping defined by a semi-infinite system of equalities and inequalities. Based on this formula, we prove a theorem of Eckart-Young type for such set-valued infinite-dimensional mappings: given a metrically regular mapping F of this kind, the infimum of the norm of a linear function g such that F… (More)

We consider the optimization problem (P A) inf x∈X {f (x) + g(Ax)} where f and g are proper convex functions defined on locally convex Hausdorff topological vector spaces X and Y respectively, and A is a linear operator from X to Y. By using the properties of the epigraph of the conjugated functions, some sufficient and necessary conditions for the strong… (More)

A semi-infinite programming problem is an optimization problem in which finitely many variables appear in infinitely many constraints. This model naturally arises in an abundant number of applications in different fields of mathematics, economics and engineering. The paper, which intends to make a compromise between an introduction and a survey, treats the… (More)

We provide a rule to calculate the subdifferential of the pointwise supremum of an arbitrary family of convex functions defined on a real locally convex topological vector space. Our formula is given exclusively in terms of the data functions, and does not require any assumption either on the index set on which the supremum is taken or on the involved… (More)

This paper provides stability theorems for the feasible set of optimization problems posed in locally convex topological vector spaces. The problems considered in this paper have an arbitrary number of inequality constraints and one constraint set. Di¤erent models are discussed, depending on the properties of the constraint functions (linear or not, convex… (More)