Quadratic convergence in a primal-dual method
Mathematics of Operations Research
On adaptive-step primal-dual interior-point algorithms for linear programming
Mathematics of Operations Research
A quadratically convergent OnL -iteration algorithm for linear programming
Mathematical Programming: Series A and B
Local convergence of interior-point algorithms for degenerate monotone LCP
Computational Optimization and Applications
Efficient hybrid algorithms for finding zeros of convex functions
Journal of Complexity
On quadratic and OnL convergence of a predictor-corrector algorithm for LCP
Mathematical Programming: Series A and B
Journal of Optimization Theory and Applications
The curvature integral and the complexity of linear complementarity problems
Mathematical Programming: Series A and B
A superquadratic infeasible-interior-point method for linear complementarity problems
Mathematical Programming: Series A and B
Convergence of interior point algorithms for the monotone linear complementarity problem
Mathematics of Operations Research
Mathematics of Operations Research
The largest step path following algorithm for monotone linear complementarity problems
Mathematical Programming: Series A and B
Mathematical Programming: Series A and B - Special issue: interior point methods in theory and practice
Mathematics of Operations Research
Superlinearly convergent infeasible-interior-point algorithm for degenerate LCP
Journal of Optimization Theory and Applications
High Order Infeasible-Interior-Point Methods for Solving Sufficient Linear Complementarity Problems
Mathematics of Operations Research
Infeasible-interior-point paths for sufficient linear complementarity problems and their analyticity
Mathematical Programming: Series A and B
Mathematics of Operations Research
A Large-Step Infeasible-Interior-Point Method for the P*-Matrix LCP
SIAM Journal on Optimization
A Quadratically Convergent Infeasible-Interior-Point Algorithm for LCP with Polynomial Complexity
SIAM Journal on Optimization
Mathematical Programming: Series A and B
The Kantorovich Theorem and interior point methods
Mathematical Programming: Series A and B
SIAM Journal on Optimization
Mathematical Programming: Series A and B
Primal-Dual Affine Scaling Interior Point Methods for Linear Complementarity Problems
SIAM Journal on Optimization
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A new class of infeasible interior point methods for solving sufficient linear complementarity problems (LCPs) requiring one matrix factorization and $m$ backsolves at each iteration is proposed and analyzed. The algorithms from this class use a large $({\cal N}_\infty^-$) neighborhood of an infeasible central path associated with the complementarity problem and an initial positive, but not necessarily feasible, starting point. The Q-order of convergence of the complementarity gap, the residual, and the iteration sequence is $m+1$ for problems that admit a strict complementarity solution and $(m+1)/2$ for general sufficient LCPs. The methods do not depend on the handicap $\kappa$ of the sufficient LCP. If the starting point is feasible (or “almost” feasible), the proposed algorithms have ${\cal O}((1+\kappa)(1+\log\sqrt[m]{1+\kappa}\,)\sqrt{n}\;L)$ iteration complexity, while if the starting point is “large enough,” the iteration complexity is ${\cal O}((1+\kappa)^{2+1/m}(1+\log\sqrt[m]{1+\kappa}\,)n\;L)$.