In this work, we propose a predictor-corrector interior point method for linear programming in a primal-dual context, where the next iterate is chosen by the minimization of a polynomial merit function of three variables: the first is the steplength, the second defines the central path and the third models the weight of a corrector direction. The merit function minimization is performed by rest...

There has been a great deal of success in the last twenty years with the use of cutting plane algorithms to solve specialized integer programming problems. Generally, these algorithms work by solving a sequence of linear programming relaxations of the integer programming problem, and they use the simplex algorithm to solve the relaxations. In this paper, we describe experiments using a predicto...

In this paper, we use the auxiliary principle technique in conjunction with the Bregman function to suggest and analyze a three-step predictor-corrector method for solving mixed quasi variational-like inequalities. We also study the convergence criteria of this new method under some mild conditions. As special cases, we obtain various new and known methods for solving variational inequalities a...

In the present paper we present a methodology that is applicable to large-eddy simulations of fluid structure interaction problems. The fluid flow equations are solved on a fixed grid that does not conform to the structure, and boundary conditions are imposed using a local reconstruction procedure. The structure that undergoes both linear-elastic and large-angle/large-displacement rigid body mo...

A grid model was developed to combine small-scale grid resolution and long-term predictions of radionuclide dispersion in shallow seas. A predictor-corrector algorithm ensures an unconditional stability of the model. Four modules calculate the concentration of suspended sediments, the dispersion of radionuclides in the marine environment, and the doses to members of the public and marine biota....

In this paper we present a variant of Vavasis and Ye’s layered-step path following primaldual interior-point algorithm for linear programming. Our algorithm is a predictor-corrector type algorithm which uses from time to time the least layered squares (LLS) direction in place of the affine scaling direction. It has the same iteration-complexity bound of Vavasis and Ye’s algorithm, namely O(n3.5...

Motivated by a numerical example which shows that a feasible version of Mehrotra’s original predictor-corrector algorithm might be inefficient in practice, Salahi et al., proposed a so-called safeguard based variant of the algorithm that enjoys polynomial iteration complexity while its practical efficiency is preserved. In this paper we analyze the same Mehrotra’s algorithm from a different per...

We introduce a new class of numerical schemes for the solution of the Cauchy problem for non-stiff ordinary differential equations (ODEs). Our algorithms are of the predictor-corrector type; they are obtained via the decomposition of the solutions of the ODEs into combinations of appropriately chosen exponentials, whereas the classical schemes are based on the approximation of solutions by poly...