Francisco Guerra Vázquez

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This paper deals with the class of generalized semi-infinite programming problems (GSIPs) in which the index set of the inequality constraints depends on the decision vector and all emerging functions are assumed to be continuously differentiable. We introduce two extensions of the Kuhn–Tucker constraint qualification (which is based on the existence of a(More)
We consider the maximum function f resulting from a finite number of smooth functions. The logarithmic barrier function of the epigraph of f gives rise to a smooth approximation gε of f itself, where ε > 0 denotes the approximation parameter. The one-parametric family gε converges – relative to a compact subset – uniformly to the function f as ε tends to(More)
Convex vector (or multi-objective) semi-infinite optimization deals with the simultaneous minimization of finitely many convex scalar functions subject to infinitely many convex constraints. This paper provides characterizations of the weakly efficient, efficient and properly efficient points in terms of cones involving the data and Karush-Kuhn-Tucker(More)
We consider semi-infinite programming problems SIP(z) depending on a finite dimensional parameter z ∈ Rp. Provided that x̄ is a strongly stable stationary point of SIP(z̄), there exists a locally unique and continuous stationary point mapping z → x(z). This defines the local critical value function φ(z) := f (x(z); z), where x → f (x; z) denotes the(More)
We consider unconstrained finite dimensional multi-criteria optimization problems, where the objective functions are continuously differentiable. Motivated by previous work of Brosowski and da Silva (1994), we suggest a number of tests (TEST 1–4) to detect, whether a certain point is a locally (weakly) efficient solution for the underlying vector(More)