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Showing 3 results for Kheirfam
Dr. Behrouz Kheirfam,
Volume 4, Issue 1 (5-2013)
Abstract
We present a new full Nesterov and Todd step infeasible interior-point algorithm for semi-definite optimization. The algorithm decreases the duality gap and the feasibility residuals at the same rate. In the algorithm, we construct strictly feasible iterates for a sequence of perturbations of the given problem and its dual problem. Every main iteration of the algorithm consists of a feasibility step and some centering steps. We show that the algorithm converges and finds an approximate solution in polynomial time. A numerical study is made for the numerical performance. Finally, a comparison of the obtained results with those by other existing algorithms is made.
Dr. Behrouz Kheirfam,
Volume 6, Issue 2 (9-2015)
Abstract
In this paper, we propose an arc-search corrector-predictor
interior-point method for solving $P_*(kappa)$-linear
complementarity problems. The proposed algorithm searches the
optimizers along an ellipse that is an approximation of the central
path. The algorithm generates a sequence of iterates in the wide
neighborhood of central path introduced by Ai and Zhang. The
algorithm does not depend on the handicap $kappa$ of the problem,
so that it can be used for any $P_*(kappa)$-linear complementarity
problem. Based on the ellipse approximation of the central path and
the wide neighborhood, we show that the proposed algorithm has
$O((1+kappa)sqrt{n}L)$ iteration complexity, the best-known
iteration complexity obtained so far by any interior-point method
for solving $P_*(kappa)$-linear complementarity problems.
Miss Hadis Abedi , Prof Behrouz Kheirfam,
Volume 12, Issue 2 (11-2021)
Abstract
In this paper, we present a new primal-dual predictor-corrector interior-point algorithm for linear optimization problems. In each iteration of this algorithm, we use the new wide neighborhood proposed by Darvay and Takács. Our algorithm computes the predictor direction, then the predictor direction is used to obtain the corrector direction. We show that the duality gap reduces in both predictor and corrector steps. Moreover, we conclude that the complexity bound of this algorithm coincides with the best-known complexity bound obtained for small neighborhood algorithms. Eventually, numerical results show the capability and efficiency of the proposed algorithm.
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