QPCOMP is an extremely robust algorithm for solving mixed nonlinear complementarity problems that has fast local convergence behavior. Based in part on the NE/SQP method of Pang and Gabriell14], this algorithm represents a signiicant advance in robustness at no cost in eeciency. In particular, the algorithm is shown to solve any solvable Lipschitz continuous, continuously diierentiable, pseudo-...

This paper describes several methods for solving nonlinear complementarity problems. A general duality framework for pairs of monotone operators is developed and then applied to the monotone complementarity problem, obtaining primal, dual, and primal-dual formulations. We derive Bregman-function-based generalized proximal algorithms for each of these formulations, generating three classes of co...

Let M n (IK) denote the set of all n n matrices with elements in IK, where IK represents the eld IR of real numbers, the eld 0 C of complex numbers or the (noncommutative) eld IH of quaternion numbers. We call a subset T of M n (IK) a *-subalgebra of M n (IK) over the eld IR (or simply a *-subalgebra) if (i) T forms a subring of M n (IK) with the usual addition A + B and multiplication AB of ma...

A modiied predictor-corrector algorithm is proposed for solving monotone linear complementarity problems from infeasible starting points. The algorithm terminates in O(nL) steps either by nding a solution or by determining that the problem is not solvable. The complexity of the algorithm depends on the quality of the starting point. If the problem is solvable and if a certain measure of feasibi...

A large-step infeasible-interior-point method is proposed for solving P∗(κ)-matrix linear complementarity problems. It is new even for monotone LCP. The algorithm generates points in a large neighborhood of an infeasible central path. Each iteration requires only one matrix factorization. If the problem is solvable, then the algorithm converges from arbitrary positive starting points. The compu...

An interior point method (IPM) defines a search direction at an interior point of the feasible region. These search directions form a direction field which in turn defines a system of ordinary differential equations (ODEs). Thus, it is natural to define the underlying paths of the IPM as the solutions of the systems of ODEs. In [8], these off-central paths are shown to be well-defined analytic ...

An interior point method (IPM) defines a search direction at each interior point of the feasible region. These search directions form a direction field which in turn gives rise to a system of ordinary differential equations (ODEs). Thus, it is natural to define the underlying paths of the IPM as the solutions of the system of ODEs. In [9], these offcentral paths are shown to be well-defined ana...