A Modiied O(nl) Infeasible-interior-point Algorithm for Lcp with Quadratic Convergence
نویسندگان
چکیده
A modiied predictor-corrector algorithm is proposed for solving monotone linear complementarity problems from infeasible starting points. The algorithm terminates in O(nL) steps either by nding a solution or by determining that the problem is not solvable. The complexity of the algorithm depends on the quality of the starting point. If the problem is solvable and if a certain measure of feasibility at the starting point is small enough then the algorithm nds a solution in O(p nL) iterations. The algorithm requires two matrix factorizations and two backsolves per iteration. If the problem has a strictly complementary solution then the algorithm is quadratically convergent, and therefore its asymptotic eeciency index is p 2.
منابع مشابه
An O(nL) infeasible-interior-point algorithm for LCP with quadratic convergence*
The Mizuno-Todd-Ye predictor-corrector algorithm for linear programming is extended for solving monotone linear complementarity problems from infeasible starting points. The proposed algorithm requires two matrix factorizations and at most three backsolves per iteration. Its computational complexity depends on the quality of the starting point. If the starting points are large enough, then the ...
متن کاملGlobal convergence of an inexact interior-point method for convex quadratic symmetric cone programming
In this paper, we propose a feasible interior-point method for convex quadratic programming over symmetric cones. The proposed algorithm relaxes the accuracy requirements in the solution of the Newton equation system, by using an inexact Newton direction. Furthermore, we obtain an acceptable level of error in the inexact algorithm on convex quadratic symmetric cone programmin...
متن کاملAn Infeasible{interior{point Method for the P -matrix Lcp
A predictor-corrector method for solving the P (k)-matrix linear complementarity problems from infeasible starting points is analyzed. Two matrix factorizations and at most three backsolves are to be computed at each iteration. The computational complexity depends on the quality of the starting points. If the starting points are large enough then the algorithm has O ? (+ 1) 2 nL iteration compl...
متن کاملA Superlinearly Convergent O( P Nl)-iteration Algorithm for Linear Programming
In this note we consider a large step modiication of the Mizuno-Todd-Ye O(p nL) predictor-corrector interior-point algorithm for linear programming. We demonstrate that the modiied algorithm maintains its O(p nL)-iteration complexity, while exhibiting superlinear convergence for general problems and quadratic convergence for non-degenerate problems. To our knowledge, this is the rst constructio...
متن کاملOn the Convergence of the Iteration Sequence of Infeasible Path following Algorithms for Linear Complementarity Problems (revised Version)
A generalized class of infeasible-interior-point methods for solving horizontal linear complementarity problem is analyzed and suucient conditions are given for the convergence of the sequence of iterates produced by methods in this class. In particular it is shown that the largest step path following algorithms generates convergent iterates even when starting from infeasible points. The comput...
متن کامل