In this paper, we present a primal-dual interior point algorithm for linearly constrained convex optimization (LCCO). The algorithm uses only full-Newton step to update iterates with an appropriate proximity measure f...
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In this paper, we present a primal-dual interior point algorithm for linearly constrained convex optimization (LCCO). The algorithm uses only full-Newton step to update iterates with an appropriate proximity measure for controlling feasible iterations near the central path during the solution process. The favorable polynomial complexity bound for the algorithm with short-step method is obtained, namely O(root n log n/epsilon) which is as good as the linear and convex quadratic optimization analogue. Numerical results are reported to show the efficiency of the algorithm.
In this paper, we propose a weighted short-stepprimal-dual interior point algorithm for solving monotone linear complementarity problem (LCP). The algorithm uses at each interior point iteration a full-Newton step an...
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In this paper, we propose a weighted short-stepprimal-dual interior point algorithm for solving monotone linear complementarity problem (LCP). The algorithm uses at each interior point iteration a full-Newton step and the strategy of the central path to obtain an epsilon-approximate solution of LCP. This algorithm yields the best currently well-known theoretical complexity iteration bound, namely, O(root n log n/epsilon) which is as good as the bound for the linear optimization analogue. The implementation of the algorithm and the algorithm in Wang et al. (Fuzzy Inform Eng 54:479-487, 2009) is done followed by a comparison between these two obtained numerical results.
In this paper, a short-step feasible primal-dual path-following interior point algorithm is proposed for solving a convex quadratic semidefinite optimization (CQSDO) problem. The algorithm uses at each iteration full ...
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In this paper, a short-step feasible primal-dual path-following interior point algorithm is proposed for solving a convex quadratic semidefinite optimization (CQSDO) problem. The algorithm uses at each iteration full Nesterov-Todd (NT) steps to find an c-approximated solution of CQSDO. The favorable iteration bound, namely O(root n log n/epsilon) is obtained for short-step method and which is as good as the linear and semidefinite optimization analogue. (C) 2013 Elsevier Inc. All rights reserved.
In this paper, a weighted short-stepprimal-dual path-following interior-point algorithm for solving linear optimization (LO) is presented. The algorithm uses at each interior-point iteration a full-Newton step, thus ...
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In this paper, a weighted short-stepprimal-dual path-following interior-point algorithm for solving linear optimization (LO) is presented. The algorithm uses at each interior-point iteration a full-Newton step, thus no need to use line search, and the strategy of the central-path to obtain an epsilon-approximated solution of LO. We show that the algorithm yields the iteration bound, namely, O(root n log n/epsilon). This bound is currently the best iteration bound for LO. Finally, some numerical results are reported in order to analyze the efficiency of the proposed algorithm.
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