Finite Convergence of A Subgradient Projections Method with Expanding Controls
نویسندگان
چکیده
We study finite convergence of the modified cyclic subgradient projections (MCSP) algorithm for the convex feasibility problem (CFP) in the Euclidian space. Expanding control sequences allow the indices of the sets of the CFP to re-appear and be used again by the algorithm ∗Currently with the Department of Radiation Oncology, Massachusetts General Hospital and Harvard Medical School, Boston, Massachusetts 02114, USA.
منابع مشابه
An acceleration scheme for cyclic subgradient projections method
An algorithm for solving convex feasibility problem for a finite family of convex sets is considered. The acceleration scheme of De Pierro (em Methodos de projeção para a resolução de sistemas gerais de equações algébricas lineares. Thesis (tese de Doutoramento), Instituto de Matemática da UFRJ, Cidade Universitária, Rio de Janeiro, Brasil, 1981), which is designed for simultaneous algorithms, ...
متن کاملA new Levenberg-Marquardt approach based on Conjugate gradient structure for solving absolute value equations
In this paper, we present a new approach for solving absolute value equation (AVE) whichuse Levenberg-Marquardt method with conjugate subgradient structure. In conjugate subgradientmethods the new direction obtain by combining steepest descent direction and the previous di-rection which may not lead to good numerical results. Therefore, we replace the steepest descentdir...
متن کاملSeminorm-Induced Oblique Projections for Sparse Nonlinear Convex Feasibility Problems
Simultaneous subgradient projection algorithms for the convex feasibility problem use subgradient calculations and converge sometimes even in the inconsistent case. We devise an algorithm that uses seminorm-induced oblique projections onto super half-spaces of the convex sets, which is advantageous when the subgradient-Jacobian is a sparse matrix at many iteration points of the algorithm. Using...
متن کاملOn The Behavior of Subgradient Projections Methods for Convex Feasibility Problems
We study some methods of subgradient projections for solving a convex feasibility problem with general (not necessarily hyperplanes or half-spaces) convex sets in the inconsistent case and propose a strategy that controls the relaxation parameters in a specific self-adapting manner. This strategy that controls the relaxation parameters in a specific manner leaves enough user-flexibility but giv...
متن کاملRadial Subgradient Descent
We present a subgradient method for minimizing non-smooth, non-Lipschitz convex optimization problems. The only structure assumed is that a strictly feasible point is known. We extend the work of Renegar [1] by taking a different perspective, leading to an algorithm which is conceptually more natural, has notably improved convergence rates, and for which the analysis is surprisingly simple. At ...
متن کامل