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The plain Newton-min algorithm to solve the linear complementarity problem (LCP for short) 0 ≤ x ⊥ (M x + q) ≥ 0 can be viewed as a semismooth Newton algorithm without globalization technique to solve the system of piecewise linear equations min(x, M x + q) = 0, which is equivalent to the LCP. When M is an M-matrix of order n, the algorithm is known to… (More)

The modeling of migration of hydrogen produced by the corrosion of the nuclear waste packages in an underground storage including the dissolution of hydrogen involves a set of nonlinear partial differential equations with nonlinear complementarity constraints. This article shows how to apply a modern and efficient solution strategy, the Newton-min method,… (More)

- Ibtihel Ben Gharbia, Jean Charles Gilbert, J. Charles Gilbert, Ben Gharbia
- 2015

Nonconvergence of the plain Newton-min algorithm for linear complementarity problems with a P-matrix — The full report.. HAL is a multidisciplinary open access archive for the deposit and dissemination of scientific research documents, whether they are published or not. The documents may come from teaching and research institutions in France or abroad, or… (More)

It is shown that a nondegenerate square real matrix M is a P-matrix if and only if, whatever is the real vector q, the Newton-min algorithm does not cycle between two points when it is used to solve the linear complementarity problem 0 x ⊥ (M x + q) 0.

- J. Charles Gilbert, P -matrix, Ibtihel Ben Gharbia
- 2010

The plain Newton-min algorithm to solve the linear complementarity problem (LCP for short) 0 x ⊥ (M x + q) 0 can be viewed as a nonsmooth Newton algorithm without globalization technique to solve the system of piecewise linear equations min(x, M x + q) = 0, which is equivalent to the LCP. When M is an M-matrix of order n, the algorithm is known to converge… (More)

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