This paper is devoted to the study of a new class of nonconvex variational inequalities, named general regularized nonconvex variational inequalities. By using the auxiliary principle technique, a new modified predictor–corrector iterative algorithm for solving general regularized nonconvex variational inequalities is suggested and analyzed. The convergence of the iterative algorithm is establi...

h this paper, we use the auxiliary principle technique to suggest a new &ass of predictor-corrector algorithms for solving generalized variational inequalities. The convergence of the proposed method only requires the partially relaxed strongly monotonicity of the operator, which is weaker than co-coercivity. As special cases, we obtain a number of known and new results for solving va,rious cla...

In this paper a one parameter predictor–corrector method, which we call it A-EBDF, is introduced and analyzed. With a modification of A-BDF and EBDF methods we propose a multistep method whose region of absolute stability is larger than those of A-BDF and EBDF methods. © 2004 IMACS. Published by Elsevier B.V. All rights reserved. MSC: 65L05

This paper presents a predictor-corrector algorithm for solving the strongly nonlinear general noncovex variational inequality, which is a class of nonconvex variational inequalities involving three nonlinear operators. We establish the equivalence between the strongly nonlinear general nonconvex variational inequalities and the fixed point problem, and show that the convergence of the predicto...

A family of Enright’s second derivative formulas with trigonometric basis functions is derived using multistep collocation method. The continuous schemes obtained are used to generate complementary methods. The stability properties of the methods are discussed.Themethodswhich can be applied in predictor-corrector formare implemented in block formas simultaneous numerical integrators over nonove...

This paper addresses the role of centrality in the implementation of interior point methods. We provide theoretical arguments to justify the use of a symmetric neighbourhood, and translate them into computational practice leading to a new insight into the role of recentering in the implementation of interior point methods. Second-order correctors, such as Mehrotra’s predictor–corrector, can occ...

A predictor-corrector method for solving linear programs from infeasible starting points is analyzed. The method is quadratically convergent and can be combined with Ye's finite termination scheme under very general assumptions. If the starting points are large enough then the algorithm has O(nL) iteration complexity. If the ratio between feasibility and optimality at the starting points is sma...