Polyhedral Newton-min algorithms for complementarity problems

The semismooth Newton method is a very efficient approach for computing a zero of a large class of nonsmooth equations. When the initial iterate is sufficiently close to a regular zero and the function is strongly semismooth, the generated sequence converges quadratically to that zero, while the iteration only requires to solve a linear system. … Read more

Exact computation of an error bound for a generalized linear complementarity problem with unique solution

This paper considers a generalized form of the standard linear complementarity problem with unique solution and provides a more precise expression of an upper error bound discovered by Chen and Xiang in 2006. This expression has at least two advantages. It makes possible the exact computation of the error bound factor and it provides a … Read more

An algorithmic characterization of P-matricity II: adjustments, refinements, and validation

The paper “An algorithmic characterization of P-matricity” (SIAM Journal on Matrix Analysis and Applications, 34:3 (2013) 904–916, by the same authors as here) implicitly assumes that the iterates generated by the Newton-min algorithm for solving a linear complementarity problem of dimension n, which reads 0 ⩽ x ⊥ (M x + q) ⩾ 0, are … Read more

A lower bound on the iterative complexity of the Harker and Pang globalization technique of the Newton-min algorithm for solving the linear complementarity problem

The plain Newton-min algorithm for solving the linear complementarity problem (LCP) 0 ≤ x ⊥ (Mx+q) ≥ 0 can be viewed as an instance of the plain semismooth Newton method on the equational version min(x,Mx+q) = 0 of the problem. This algorithm converges for any q when M is an M-matrix, but not when it … Read more

An algorithmic characterization of P-matricity

It is shown that a matrix $M$ is a P-matrix if and only if, whatever is the vector $q$, the Newton-min algorithm does not cycle between two points when it is used to solve the linear complementarity problem $0\leq x\perp (Mx+q)\geq0$. Citation Inria research report RR-8004 Article Download View An algorithmic characterization of P-matricity

An EP theorem for dual linear complementarity problem

The linear complementarity problem (LCP) belongs to the class of NP-complete problems. Therefore we can not expect a polynomial time solution method for LCPs without requiring some special property of the matrix of the problem. We show that the dual LCP can be solved in polynomial time if the matrix is row sufficient, moreover in … Read more