A path following method for LCP withsuperlinearly convergent iteration sequence

Florian Potra and Rongqin Sheng

Annals of Operations Research, 1998, vol. 81, issue 0, 97-114

Abstract: A new algorithm for solving linear complementarity problems with sufficient matrices isproposed. If the problem has a solution, the algorithm is superlinearly convergent from anypositive starting points, even for degenerate problems. Each iteration requires only onematrix factorization and at most two backsolves. Only one backsolve is necessary if theproblem is known to be nondegenerate. The algorithm generates points in a large neighborhoodof the central path and has the lowest iteration complexity obtained so far in theliterature. Moreover, the iteration sequence converges superlinearly to a maximal solutionwith the same Q-order as the complementarity sequence. Copyright Kluwer Academic Publishers 1998

Date: 1998
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DOI: 10.1023/A:1018942131812

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