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A simplified homogeneous and selfdual linear programming algorithm and its implementation
 Annals of Operations Research
, 1996
"... 1 Introduction Consider the linear programming (LP) problem in the standard form: (LP) minimize cT x ..."
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Cited by 56 (5 self)
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1 Introduction Consider the linear programming (LP) problem in the standard form: (LP) minimize cT x
An infeasibleinteriorpoint method for the P*matrix LCP
, 1994
"... A predictorcorrector 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 poi ..."
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Cited by 3 (3 self)
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A predictorcorrector 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 \Gamma ( + 1) 2 nL \Delta iteration complexity. If a certain measure of feasibility at the starting point is small enough then the algorithm has O (( + 1) p nL) iteration complexity. Both "feasibility' and "optimality" are reduced exactly at the same rate. The algorithm is quadratically convergent for problems having a strictly complementary solution, and therefore its asymptotic efficiency index is p 2 Key Words: Linear complementarity problems, predictorcorrector, infeasibleinteriorpoint algorithm, polynomiality, superlinear convergence. Abbreviated Title: An infeasibleinteriorpoint method for LCP. Dep...