We study the multiple-sets split feasibility problem that requires to find a point closest to a family of closed convex sets in one space such that its image under a linear transformation will be closest to another family of closed convex sets in the image space. By casting the problem into an equivalent problem in … Read more
We present a target-following framework for semidefinite programming, which generalizes the target-following framework for linear programming. We use this framework to build weighted path-following interior-point algorithms of three distinct flavors: short-step, predictor-corrector, and large-update. These algorithms have worse-case iteration bounds that parallel their counterparts in linear programming. We further consider the problem of finding analytic … Read more
This paper extends the full convergence of the steepest descent algorithm with a generalized Armijo search and a proximal regularization to solve quasiconvex minimization problems defined on complete Riemannian manifolds. Previous convergence results are obtained as particular cases of our approach and some examples in non Euclidian spaces are given. CitationJ. Math. Anal. Appl. 341 … Read more
In this paper a new derivative-free method is developed for solving unconstrained nonsmooth optimization problems. This method is based on the notion of a discrete gradient. It is demonstrated that the discrete gradients can be used to approximate subgradients of a broad class of nonsmooth functions. It is also shown that the discrete gradients can … Read more
In this paper we extend in a simple way the transformation of Charnes and Cooper to the case where the functional ratio to be considered are of similar polynomial CitationUniversidad de San Luis Ejercito de Los Andes 950 San Luis(5700) ArgentinaArticleDownload View PDF
In this paper we establish criteria for the stability of the proximal mapping \textrm{Prox} $_{\varphi }^{f}=(\partial \varphi +\partial f)^{-1}$ associated to the proper lower semicontinuous convex functions $\varphi $ and $f$ on a reflexive Banach space $X.$ We prove that, under certain conditions, if the convex functions $\varphi _{n}$ converge in the sense of Mosco … Read more
This paper generalizes the proximal point method using Bregman distances to solve convex and quasiconvex optimization problems on noncompact Hadamard manifolds. We will proved that the sequence generated by our method is well defined and converges to an optimal solution of the problem. Also, we obtain the same convergence properties for the classical proximal method, … Read more
The minimization of an objective function over a constraint set can often be simplified if the “active manifold” of the constraints set can be correctly identified. In this work we present a simple subproblem, which can be used inside of any (convergent) optimization algorithm, that will identify the active manifold of a “prox-regular partly smooth” … Read more
The major focus of this work is to compare several methods for computing the proximal point of a nonconvex function via numerical testing. To do this, we introduce two techniques for randomly generating challenging nonconvex test functions, as well as two very specific test functions which should be of future interest to Nonconvex Optimization Benchmarking. … Read more
Based on previous explicit computations of universal barrier functions, we describe numerical experiments for solving certain classes of convex optimization problems. The comparison is given of the performance of the classical affine-scaling algorithm with similar algorithm based upon the universal barrier function CitationTo appear in “Computational Optimization and Applications”ArticleDownload View PDF