In this paper, we propose a new method for solving nonlinear complementarity problems (NCP), where the underlying function F is pseudomonotone and continuous. The method can be viewed as an extension of the method of ...
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In this paper, we propose a new method for solving nonlinear complementarity problems (NCP), where the underlying function F is pseudomonotone and continuous. The method can be viewed as an extension of the method of Noor and Bnouhachem (2006) 113], by performing an additional projection step at each iteration and another optimal step length is employed to reach substantial progress in each iteration. We prove the global convergence of the proposed method under some suitable conditions. Some numerical results are given to illustrate the efficiency and the implementation of the new proposed method. (C) 2009 Elsevier Ltd. All rights reserved.
We extend epsilon-subgradient descent methods for unconstrained nonsmooth convex minimization to constrained problems over polyhedral sets, in particular over R-+(p). This is done by replacing the usual squared quadra...
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We extend epsilon-subgradient descent methods for unconstrained nonsmooth convex minimization to constrained problems over polyhedral sets, in particular over R-+(p). This is done by replacing the usual squared quadratic regularization term used in subgradient schemes by the logarithmic-quadratic distancelike function recently introduced by the authors. We then obtain interior epsilon-subgradient descent methods, which allow us to provide a natural extension of bundle methods and Polyak's subgradient projection methods for nonsmooth convex minimization. Furthermore, similar extensions are considered for smooth constrained minimization to produce interior gradient descent methods. Global convergence as well as an improved global efficiency estimate are established for these methods within a unifying principle and minimal assumptions on the problem's data.
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