Regina Sandra Burachik

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Given a point-to-set operator T, we introduce the operator T " deened as T " (x) = fu : hu ? v; x ? yi 0 for all y 2 R n ; v 2 T(y)g. When T is maximal monotone T " inherits most properties of the "-subdiierential, e.g. it is bounded on bounded sets, T " (x) contains the image through T of a suuciently small ball around x, etc. We prove these and other(More)
In 1951, Fenchel discovered a special duality, which relates the minimization of a sum of two convex functions with the maximization of the sum of concave functions, using conjugates. Fenchel’s duality is central to the study of constrained optimization. It requires an existence of an interior point of a convex set which often has empty interior in(More)
We propose a new kind of inexact scheme for a family of generalized proximal point methods for the monotone complementarity problem. These methods, studied by Auslender, Teboulle and Ben-Tiba, converge under the sole assumption of existence of solutions. We prove convergence of our new scheme, as well as discuss its implementability.
We consider a generalized proximal point method (GPPA) for solving the nonlinear complementarity problem with monotone operators in R ' \ lt differs from the classical proximal point method discussed by Rockafellar for the problem offinding zeroes of monotone operators in the use of generalized distances, called (p-divergences, instead of the Euclidean one.(More)
In this paper we show the weak convergence and stability of the proximal point method when applied to the constrained convex optimization problem in uniformly convex and uniformly smooth Banach spaces. In addition, we establish a nonasymptotic estimate of convergence rate of the sequence of functional values for the unconstrained case. This estimate depends(More)