D. Benterki, B. Merikhi (2001)
RAIRO - Operations Research - Recherche Opérationnelle
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In this note, we present a slight modification of an algorithm for the strict feasibility problem. This modification reduces the number of iterations.
Djamel Benterki, Jean-Pierre Crouzeix, Bachir Merikhi (2007)
RAIRO - Operations Research
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This paper presents a feasible primal algorithm for linear semidefinite programming. The algorithm starts with a strictly feasible solution, but in case where no such a solution is known, an application of the algorithm to an associate problem allows to obtain one. Finally, we present some numerical experiments which show that the algorithm works properly.
Wei, Z., Qi, L., Birge, J.R. (1998)
Journal of Inequalities and Applications [electronic only]
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Paulo J.S. Silva, Carlos Humes (2007)
RAIRO - Operations Research
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We present an inexact interior point proximal method to solve linearly constrained convex problems. In fact, we derive a primal-dual algorithm to solve the KKT conditions of the optimization problem using a modified version of the rescaled proximal method. We also present a pure primal method. The proposed proximal method has as distinctive feature the possibility of allowing inexact inner steps even for Linear Programming. This is achieved by using an error criterion that ...
Yuan, Gonglin, Meng, Shide, Wei, Zengxin (2009)
Advances in Operations Research
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Li Sun, Guoping He, Yongli Wang, Changyin Zhou (2011)
Applications of Mathematics
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A new algorithm for solving large scale bound constrained minimization problems is proposed. The algorithm is based on an accurate identification technique of the active set proposed by Facchinei, Fischer and Kanzow in 1998. A further division of the active set yields the global convergence of the new algorithm. In particular, the convergence rate is superlinear without requiring the strict complementarity assumption. Numerical tests demonstrate the efficiency and performance of the...
Zhen-Jun Shi, Xiang-Sun Zhang, Jie Shen (2007)
RAIRO - Operations Research
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In this paper, we propose a new class of adaptive trust region methods for unconstrained optimization problems and develop some convergence properties. In the new algorithms, we use the current iterative information to define a suitable initial trust region radius at each iteration. The initial trust region radius is more reasonable in the sense that the trust region model and the objective function are more consistent at the current iterate. The global convergence, super-linear and...