A Mehrotra-Type Predictor-Corrector Algorithm for P∗(κ) Linear Complementarity Problems
نویسندگان
چکیده
Mehrotra-type predictor-corrector algorithm, as one of most efficient interior point methods, has become the backbones of most optimization packages. Salahi et al. proposed a cut strategy based algorithm for linear optimization that enjoyed polynomial complexity and maintained its efficiency in practice. We extend their algorithm to P∗(κ) linear complementarity problems. The way of choosing corrector direction for our algorithm is different from theirs. The new algorithm has been proved to have an O((1 + 4κ)(17 + 19κ) √ 1 + 2κn 3 2 log (x )s ε ) worst case iteration complexity bound. An numerical experiment verifies the feasibility of the new algorithm.
منابع مشابه
A First Order Predictor-corrector Infeasible Interior Point Method for Sufficient Linear Complementarity Problems in a Wide and Symmetric Neighborhood of the Central Path
In this paper, a new predictor-corrector method is proposed for solving sufficient linear complementarity problems (LCP) with an infeasible starting point. The method generates a sequence of iterates in a wide and symmetric neighborhood of the infeasible central path of the LCP. If the starting point is feasible or close to being feasible, then an ε-approximate solution is obtained in at most O...
متن کاملPolynomial Convergence of a Predictor-Corrector Interior-Point Algorithm for LCP
We establishe the polynomial convergence of a new class of pathfollowing methods for linear complementarity problems (LCP). Namely, we show that the predictor-corrector methods based on the L2 norm neighborhood. Mathematics Subject Classification: 90C33, 65G20, 65G50
متن کاملCorrector-predictor arc-search interior-point algorithm for $P_*(kappa)$-LCP acting in a wide neighborhood of the central path
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 de...
متن کاملCorrector-Predictor Methods for Sufficient Linear Complementarity Problems in a Wide Neighborhood of the Central Path
A higher order corrector-predictor interior-point method is proposed for solving sufficient linear complementarity problems. The algorithm produces a sequence of iterates in the N− ∞ neighborhood of the central path. The algorithm does not depend on the handicap κ of the problem. It has O((1 + κ) √ nL) iteration complexity and is superlinearly convergent even for degenerate problems.
متن کاملCorrector-predictor methods for sufficient linear complementarity problems
We present a new corrector-predictor method for solving sufficient linear complementarity problems for which a sufficiently centered feasible starting point is available. In contrast with its predictor-corrector counterpart proposed by Miao, the method does not depend on the handicap κ of the problem. The method has O((1+ κ)√nL)-iteration complexity, the same as Miao’s method, but our error est...
متن کامل