We propose in this study, a new logarithmic barrier approach to solve linear semidefinite programming problem. We are interested in computation of the direction by Newton’s method and of the displacement step using minorant functions instead of line search methods in order to reduce the computation cost.
Our new approach is even more beneficial than classical line search methods. This purpose is confirmed by some numerical simulations showing the e˙ectiveness of the algorithm developed in this work, which are presented in the last section of this paper.
In this paper, we present a logarithmic barrier interior-point method for solving a semidefinite programming problem. Newton's method is used to compute the descent direction, and minorant function are used as an efficient alternative to line search methods to determine the displacement step along the direction in order to reduce the computation cost.
We propose in this study, a new logarithmic barrier approach to solve linear programming problem. We are interested in computation of the direction by Newton's method and of the displacement step using minorant functions instead of line search methods in order to reduce the computation cost. Our new approach is even more beneficial than classical line search methods. This purpose is confirmed by many interesting numerical experimentations shown the effectiveness of the algorithm developed in this work.
The aim of this paper is to present a comparative numerical study between the minorant functions and line search methods in computing the step size in the penalty method for linear optimization. The minorant functions were confirmed by many interesting numerical experimentations to be more beneficial than the classical line search methods.
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