In this paper, we consider a feasible primal-dual interior point method for linear semidefinite programming problem (SDP) based on Alizadeh-Haeberly-Overton (AHO) direction (Monteiro, 1997). Firstly, and by a new and ...
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In this paper, we consider a feasible primal-dual interior point method for linear semidefinite programming problem (SDP) based on Alizadeh-Haeberly-Overton (AHO) direction (Monteiro, 1997). Firstly, and by a new and simple technique, we establish the existence and uniqueness of optimal solution of the perturbed problem (SDP),, and its convergence to optimal solution of (SDP). Next, we present new different alternatives to calculate the displacement step. After, we establish the convergence of the obtained algorithm and we show that its complexity is O (root n ln [epsilon(-1) (< X-0, S-0 >)]). Finally, we present some numerical simulations which show the effectiveness of the algorithm developed in this work. (C) 2016 Elsevier B.V. All rights reserved.
The parameters in the semidefiniteprogramming problems generated by the average of a sample, may lead to the deviation of the optimal value and optimal solutions due to the uncertainty of the data. The statistical pr...
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The parameters in the semidefiniteprogramming problems generated by the average of a sample, may lead to the deviation of the optimal value and optimal solutions due to the uncertainty of the data. The statistical properties of estimates of the optimal value and the optimal solutions are given in this paper, when the estimated parameters are both in the objective function and in the constraints. This analysis is mainly based on the theory of the linearprogramming and the perturbation theory of the semidefiniteprogramming.
The linear semidefinite programming problem is considered. To solve it, the variant of the primal simplex method, that generalizes the corresponding method for linearprogramming problems, is proposed. The passage fro...
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The linear semidefinite programming problem is considered. To solve it, the variant of the primal simplex method, that generalizes the corresponding method for linearprogramming problems, is proposed. The passage from one extreme point of the feasible set to another one is described. The main attention is given to pivoting in the case, when the extreme point is irregular, i.e. the "triangular" number of rank of the matrix in the basic point is less than number of equality type constraints in the problem. The approach for finding a starting extreme point is proposed too. The local convergence of the method is proven.
In this paper,we introduce for the first time a new eligible kernel function with a hyperbolic barrier term for semidefiniteprogramming(SDP).This add a new type of functions to the class of eligible kernel *** prove ...
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In this paper,we introduce for the first time a new eligible kernel function with a hyperbolic barrier term for semidefiniteprogramming(SDP).This add a new type of functions to the class of eligible kernel *** prove that the interior-point algorithm based on the new kernel function meets O(n3/4 logε/n)iterations as the worst case complexity bound for the large-update *** coincides with the complexity bound obtained by the first kernel function with a trigonometric barrier term proposed by El Ghami et ***2012,and improves with a factor n(1/4)the obtained iteration bound based on the classic kernel *** present some numerical simulations which show the effectiveness of the algorithm developed in this paper.
The purpose of this paper is to improve the complexity of a large-update primal-dual interior point method for a semidefiniteprogramming problem. We define a proximity function for the semidefiniteprogramming proble...
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The purpose of this paper is to improve the complexity of a large-update primal-dual interior point method for a semidefiniteprogramming problem. We define a proximity function for the semidefiniteprogramming problem based on a new parametric kernel function and prove that the worst-case iteration bound for the new correspondent algorithm is O (root n (lnn)(pq+1/pq) ln n/epsilon), where p,q >= 1.
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