The existing methods of projection for solving convex feasibility problem may lead to slow conver- gence when the sequences enter some narrow＂corridor＂ between two or more convex sets. In this paper, we apply a tech...
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The existing methods of projection for solving convex feasibility problem may lead to slow conver- gence when the sequences enter some narrow＂corridor＂ between two or more convex sets. In this paper, we apply a technique that may interrupt the monotonity of the constructed sequence to the sequential subgradient pro- jection algorithm to construct a nommonotonous sequential subgradient projection algorithm for solving convex feasibility problem, which can leave such corridor by taking a big step at different steps during the iteration. Under some suitable conditions, the convergence is *** also compare the numerical performance of the proposed algorithm with that of the monotonous algorithm by numerical experiments.
In this paper, the subgradientprojection iteration is used to find an approximation solution of a weighted least-squares problem with respect to linear imaging system. Instead of an exact or approximate line search i...
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In this paper, the subgradientprojection iteration is used to find an approximation solution of a weighted least-squares problem with respect to linear imaging system. Instead of an exact or approximate line search in each iteration, the step length in this paper is fixed by the weighted least-square function and the current iteration. Using weighted singular value decomposition, we estimate the bounds of step length. Consequently, we provide the decreasing property and the sufficient condition for convergence of the iterative algorithm. Furthermore, we perform a numerical experiment on a two dimensional image reconstruction problem to confirm the validity of this subgradientprojection iteration.
In this paper, we propose a subgradient projection algorithm for solving the multiple-sets split equality problem (MSSEP), and investigate its linear convergence. We involve the bounded linear regularity for the MSSEP...
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In this paper, we propose a subgradient projection algorithm for solving the multiple-sets split equality problem (MSSEP), and investigate its linear convergence. We involve the bounded linear regularity for the MSSEP, and construct several sufficient conditions to ensure the linear convergence of our proposed algorithm. One of the highlights of our algorithm is that metric projections onto given feasibility sets are easily calculated (that is, the projections onto half-spaces). Some numerical results are provided to illustrate the validity of our proposed algorithm.
We study the convergence issue of the subgradientalgorithm for solving the convex feasibility problems in Riemannian manifolds, which was first proposed and analyzed by Bento and Melo [J. Optim. Theory Appl., 152 (20...
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We study the convergence issue of the subgradientalgorithm for solving the convex feasibility problems in Riemannian manifolds, which was first proposed and analyzed by Bento and Melo [J. Optim. Theory Appl., 152 (2012), pp. 773-785]. The linear convergence property about the subgradientalgorithm for solving the convex feasibility problems with the Slater condition in Riemannian manifolds are established, and some step sizes rules are suggested for finite convergence purposes, which are motivated by the work due to De Pierro Iusem [Appl. Math. Optim., 17 (1988), pp. 225-235]. As a by-product, the convergence result of this algorithm is obtained for the convex feasibility problem without the Slater condition assumption. These results extend and/or improve the corresponding known ones in both the Euclidean space and Riemannian manifolds.
In the present paper, we use subgradient projection algorithms for solving convex feasibility problems. We show that almost all iterates, generated by a subgradient projection algorithm in a Hilbert space, are approxi...
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In the present paper, we use subgradient projection algorithms for solving convex feasibility problems. We show that almost all iterates, generated by a subgradient projection algorithm in a Hilbert space, are approximate solutions. Moreover, we obtain an estimate of the number of iterates which are not approximate solutions. In a finite-dimensional case, we study the behavior of the subgradient projection algorithm in the presence of computational errors. Provided computational errors are bounded, we prove that our subgradient projection algorithm generates a good approximate solution after a certain number of iterates.
In the present paper we study convergence of subgradient projection algorithms for solving convex feasibility problems in a Hilbert space. Our goal is to obtain an approximate solution of the problem in the presence o...
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In the present paper we study convergence of subgradient projection algorithms for solving convex feasibility problems in a Hilbert space. Our goal is to obtain an approximate solution of the problem in the presence of computational errors. We show that our subgradient projection algorithm generates a good approximate solution, if the sequence of computational errors is bounded from above by a constant. (c) 2013 Elsevier Inc. All rights reserved.
In this paper, a kind of subgradient projection algorithms is established for minimizing a locally Lipschitz continuous function subject to nonlinearly smooth constraints, which is based on the idea to get a feasible ...
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