Roger Behling, Yunier Bello-Cruz, Alfredo N. Iusem, Di Liu, Luiz-Rafael Santos
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引用次数: 0
Abstract
SIAM Journal on Optimization, Volume 34, Issue 3, Page 2535-2556, September 2024. Abstract. In this paper, we present a variant of the circumcenter method for the convex feasibility problem (CFP), ensuring finite convergence under a Slater assumption. The method replaces exact projections onto the convex sets with projections onto separating half-spaces, perturbed by positive exogenous parameters that decrease to zero along the iterations. If the perturbation parameters decrease slowly enough, such as the terms of a diverging series, finite convergence is achieved. To the best of our knowledge, this is the first circumcenter method for CFP that guarantees finite convergence.
期刊介绍：
The SIAM Journal on Optimization contains research articles on the theory and practice of optimization. The areas addressed include linear and quadratic programming, convex programming, nonlinear programming, complementarity problems, stochastic optimization, combinatorial optimization, integer programming, and convex, nonsmooth and variational analysis. Contributions may emphasize optimization theory, algorithms, software, computational practice, applications, or the links between these subjects.
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