Corrector-predictor methods for sufficient linear complementarity problems (original) (raw)

Improved infeasible-interior-point algorithm for linear complementarity problems

Bulletin of The Iranian Mathematical Society, 2012

We present a modied version of the infeasible-interior- point algorithm for monotone linear complementary problems in- troduced by Mansouri et al. (Nonlinear Anal. Real World Appl. 12(2011) 545{561). Each main step of the algorithm consists of a feasibility step and several centering steps. We use a dierent feasibility step, which targets at the + -center. It results a better iteration bound.

Some numerical aspects on a method for solving linear problems with complementarity constraints

2021

A known method for solving linear problems with complementarity constraints is briefly recalled. The method decomposes the given problem in a sequence of parameterized problems and - by means of suitable cuts - allows to define an iterative procedure that leads to an optimal solution or to an approximation of it providing an estimate of the error. In this paper, for problems of different dimensions we have implemented some numerical experiments which show that in most cases the method converges linearly with respect to the dimension of the problem. Our results are also compared with those obtained by similar approaches where different kinds of cuts are considered

Infeasible penalty interior-point method for linear complementarity problems

International Journal of Informatics and Applied Mathematics, 2022

In this study, we implement a variant of infeasible interiorpoint algorithm for solving monotone linear complementarity problems (LCP). We first reformulate the monotone LCP as an minimization problem. Then a descent iterative method is applied to the latter. The descent direction is computed via the Newton method. However, for maintaining the positivity of iterates, a novel and efficient strategy is proposed. Some numerical results are reported to show the efficiency of our proposed approach.

A full-Newton step feasible interior-point algorithm for monotone horizontal linear complementarity problems

Optimization Letters, 2018

In this paper, a full-Newton step feasible interior-point algorithm is proposed for solving P * (κ)-linear complementarity problems. We prove that the full-Newton step to the central path is local quadratically convergent and the proposed algorithm has polynomial iteration complexity, namely, O (1 + 4κ) √ n log n ε , which matches the currently best known iteration bound for P * (κ)-linear complementarity problems. Some preliminary numerical results are provided to demonstrate the computational performance of the proposed algorithm.

Solution of linear complementarity problems using minimization with simple bounds

Journal of Global Optimization, 1995

We de ne a minimization problem with simple bounds associated to the horizontal linear complementarity problem (HLCP). When the HLCP is solvable, its solutions are the global minimizers of the associated problem. When the HLCP is feasible, we are able to prove a number of properties of the stationary points of the associated problem. In many cases, the stationary points are solutions of the HLCP. The theoretical results allow us to conjecture that local methods for box constrained optimization applied to the associated problem are e cient tools for solving linear complementarity problems. Numerical experiments seem to con rm this conjecture.

An iterative two-step algorithm for linear complementarity problems

Numerische Mathematik, 1994

We propose an algorithm for the numerical solution of large-scale symmetric positive-definite linear complementarity problems. Each step of the algorithm combines an application of the successive overrelaxation method with projection (to determine an approximation of the optimal active set) with the preconditioned conjugate gradient method (to solve the reduced residual systems of linear equations). Convergence of the iterates to the solution is proved. In the experimental part we compare the efficiency of the algorithm with several other methods. As test example we consider the obstacle problem with different obstacles. For problems of dimension up to 24 000 variables, the algorithm finds the solution in less then 7 iterations, where each iteration requires about 10 matrix-vector multiplications.

On the Convergence of the Iteration Sequence of Infeasible Path Following Algorithms for Linear Complementarity Problems

Mathematics of Operations Research, 1997

A generalized class of infeasible-interior-point methods for solving horizontal linear complementarity problem is analyzed and su cient conditions are given for the convergence of the sequence of iterates produced by methods in this class. In particular it is shown that the largest step path following algorithms generates convergent iterates even when starting from infeasible points. The computational complexity of the latter method is discussed in detail and its local convergent rate is analyzed. The primal-dual gap of the iterates produced by this method is superlinearly convergent to zero. A variant of the method has quadratic convergence.