In this paper, we investigate the issue of error bounds for symmetric cone complementarity problems (SCCPs). In particular, we show that the distance between an arbitrary point in Euclidean Jordan algebra and the solution set of the symmetric cone complementarity problem can be bounded above by some merit functions such as FischerBurmeister merit function, the natural residual function and the ...

Each master iteration of a simpliied Newton algorithm for solving a system of equations starts by computing the Jacobian matrix and then uses this matrix in the computation of p Newton steps: the rst of these steps is exact, and the other are called \simpliied". In this paper we apply this approach to a large step path following algorithm for monotone linear complementarity problems. The result...

A polynomial complexity bound is established for an interior point path following algorithm for the monotone linear complementarity problem that is based on the Chen{Harker{Kanzow smoothing techniques. The fundamental diierence with the Chen{Harker and Kanzow algorithms is the introduction of a rescaled Newton direction. The rescaling requires the iterates to remain in the interior of the posit...

In this paper we propose a new class of primal-dual path-following interior point algorithms for solving monotone linear complementarity problems. At each iteration, the method would select a target on the central path with a large update from the current iterate, and then the Newton method is used to get the search directions, followed by adaptively choosing the step sizes, which are e.g. the ...

An interior point method (IPM) defines a search direction at each interior point of the feasible region. The search directions at all interior points together form a direction field, which gives rise to a system of ordinary differential equations (ODEs). Given an initial point in the interior of the feasible region, the unique solution of the ODE system is a curve passing through the point, wit...

The Mizuno–Todd–Ye predictor–corrector method based on two neighborhoods DðaÞ DðaÞ of the central path of a monotone homogeneous linear complementarity problem is analyzed, where DðaÞ is composed of all feasible points with d-proximity to the central path less than or equal to a. The largest allowable value for a is 1.76. For a specific choice of a and a a lower bound of vn= ffiffiffi n p is ob...

We propose a homogeneous model for the class of mixed horizontal linear complementarity problems. The proposed homogeneous model is always solvable and provides the solution of the original problem if it exists, or a certificate of infeasibility otherwise. Our formulation preserves the sparsity of the original formulation and does not reduce to the homogeneous model of the equivalent standard l...

We present a predictor{corrector non{interior path following algorithm for the monotone linear complementarity problem based on Chen{Harker{Kanzow{Smale smoothing techniques. Although the method is modeled on the interior point predictor{ corrector strategies, it is the rst instance of a non{interior point predictor{corrector algorithm. The algorithm is shown to be both globally linearly conver...