We study the contraction-proximal point algorithm that has the following iterative form: where is a fixed element, is the resolvent operator and are all real sequences. The algorithm is known to converge strongly unde...
详细信息
We study the contraction-proximal point algorithm that has the following iterative form: where is a fixed element, is the resolvent operator and are all real sequences. The algorithm is known to converge strongly under the assumption that is bounded below away from zero and above away from 1. In this paper, we show that this condition can be further relaxed as
We consider the convergence rate of the proximal point algorithm (PPA) for finding a minimizer of proper lower semicontinuous convex functions. In the Hilbert space setting, Guler showed that the big-O rate of the PPA...
详细信息
We consider the convergence rate of the proximal point algorithm (PPA) for finding a minimizer of proper lower semicontinuous convex functions. In the Hilbert space setting, Guler showed that the big-O rate of the PPA can be improved to little-o when the sequence generated by the algorithm converges strongly to a minimizer. In this paper, we establish little-o rate of the PPA in Banach spaces without requiring this assumption. Then we apply the result to give new results on the convergence rate for sequences of alternating and averaged projections.
In this paper, the problem of solving generalized fractional programs will be addressed. This problem has been extensively studied and several algorithms have been proposed. In this work, we propose an algorithm that ...
详细信息
In this paper, the problem of solving generalized fractional programs will be addressed. This problem has been extensively studied and several algorithms have been proposed. In this work, we propose an algorithm that combines the proximalpoint method with a continuous min-max formulation of discrete generalized fractional programs. The proposed method can handle non-differentiable convex problems with possibly unbounded feasible constraints set, and solves at each iteration a convex program with unique dual solution. It generates two sequences that approximate the optimal value of the considered problem from below and from above at each step. For a class of functions, including the linear case, the convergence rate is at least linear.
The subject of this paper is the inexact proximal point algorithm of usual and Halpern type in non-positive curvature metric spaces. We study the convergence of the sequences given by the inexact proximalpoint algori...
详细信息
The subject of this paper is the inexact proximal point algorithm of usual and Halpern type in non-positive curvature metric spaces. We study the convergence of the sequences given by the inexact proximal point algorithm with non-summable errors. We also prove the strong convergence of the Halpern proximal point algorithm to a minimum point of the convex function. The results extend several results in Hilbert spaces, Hadamard manifolds and non-positive curvature metric spaces.
The proximal point algorithm is classical and popular in the community of optimization. In practice, inexact proximal point algorithms which solve the involved proximal subproblems approximately subject to certain ine...
详细信息
The proximal point algorithm is classical and popular in the community of optimization. In practice, inexact proximal point algorithms which solve the involved proximal subproblems approximately subject to certain inexact criteria are truly implementable. In this paper, we first propose an inexact proximal point algorithm with a new inexact criterion for solving convex minimization, and show its O(1/k) iteration-complexity. Then we show that this inexact proximal point algorithm is eligible for being accelerated by some influential acceleration schemes proposed by Nesterov. Accordingly, an accelerated inexact proximal point algorithm with an iteration-complexity of O(1/k (2)) is proposed.
In this paper, we present a generalized vector-valued proximal point algorithm for convex and unconstrained multi-objective optimization problems. Our main contribution is the introduction of quasi-distance mappings i...
详细信息
In this paper, we present a generalized vector-valued proximal point algorithm for convex and unconstrained multi-objective optimization problems. Our main contribution is the introduction of quasi-distance mappings in the regularized subproblems, which has important applications in the computer theory and economics, among others. By considering a certain class of quasi-distances, that are Lipschitz continuous and coercive in any of their arguments, we show that any sequence generated by our algorithm is bounded and its accumulation points are weak Pareto solutions.
In this paper we consider the proximal point algorithm to approximate a singularity of a multivalued monotone vector field on a Hadamard manifold. We study the convergence of the sequence generated by an inexact form ...
详细信息
In this paper we consider the proximal point algorithm to approximate a singularity of a multivalued monotone vector field on a Hadamard manifold. We study the convergence of the sequence generated by an inexact form of the algorithm. Our results extend the results of [3, 25] to Hadamard manifolds as well as the main result of [11] with more general assumptions on the control sequence. We also give some application to optimization.
In the paper, we introduce two iterative sequences for finding a point in the intersection of the zero set of a inverse strongly monotone or inverse-monotone operator and the zero set of a maximal monotone operator in...
详细信息
In the paper, we introduce two iterative sequences for finding a point in the intersection of the zero set of a inverse strongly monotone or inverse-monotone operator and the zero set of a maximal monotone operator in a uniformly smooth and uniformly convex Banach space. We prove weak convergence theorems under appropriate conditions, respectively. (C) 2006 Elsevier Ltd. All rights reserved.
In this paper, some proximal point algorithms ( PPAs) for maximal monotone operators in Banach spaces are considered. We obtain some results on the boundedness and the convergence of sequences generated by the PPAs wi...
详细信息
In this paper, some proximal point algorithms ( PPAs) for maximal monotone operators in Banach spaces are considered. We obtain some results on the boundedness and the convergence of sequences generated by the PPAs with some assumptions. We can also get zero of maximal f-expansive operator and maximal f-monotone at zero operator using this method and then we apply it for finding a solution of the equilibrium problem.
暂无评论