We study an infeasible interior path-following method for complemen-tarity problems. The method uses a wide neighborhood and takes one or two Newton steps per iteration. We show that the method attains global convergence, assuming the iterates are deened and bounded (which occurs when the function is a P 0-R 0-function or when the function is monotone and a suuciently positive solution exists)....

In this paper, we describe our implementation of a primal-dual infeasible-interior-point algorithm for large-scale linear programming under the MATLAB 1 environment. The resulting software is called LIPSOL { Linear-programming Interior-Point SOLvers. LIPSOL is designed to take the advantages of MATLAB's sparse-matrix functions and external interface facilities, and of existing Fortran sparse Ch...

We consider an infeasible-interior-point algorithm, endowed with a nite termination scheme, applied to random linear programs generated according to a model of Todd. Such problems have degenerate optimal solutions, and possess no feasible starting point. We use no information regarding an optimal solution in the initialization of the algorithm. Our main result is that the expected number of ite...

In this paper, we study some basic properties of the monotone semide nite nonlinear complementarity problem (SDCP). We show that the trajectory continuously accumulates into the solution set of the SDCP passing through the set of the infeasible but positive de nite matrices under certain conditions. Especially, for the monotone semide nite linear complementarity problem, the trajectory converge...

A new class of infeasible interior point methods for solving sufficient linear complementarity problems requiring one matrix factorization andm backsolves at each iteration is proposed and analyzed. The algorithms from this class use a large (N− ∞) neighborhood of an infeasible central path associated with the complementarity problem and an initial positive, but not necessarily feasible, starti...

We propose a uniied analysis for a class of infeasible-start predictor-corrector algorithms for semideenite programming problems, using the Monteiro-Zhang uniied direction. The algorithms are direct generalizations of the Mizuno-Todd-Ye predictor-corrector algorithm for linear programming. We show that the algorithms belonging to this class are globally convergent, provided the problem has a so...

Minimizing the Lennard-Jones potential, the most-studied model problem for molecular conformation, is an unconstrained global optimization problem with a large number of local minima. In this paper, the problem is reformulated as an equality constrained nonlinear programming problem with only linear constraints. This formulation allows the solution to approached through infeasible configuration...

We propose a new subgradient method for the minimization of nonsmooth convex functions over a convex set. To speed up computations we use adaptive approximate projections only requiring to move within a certain distance of the exact projections (which decreases in the course of the algorithm). In particular, the iterates in our method can be infeasible throughout the whole procedure. Neverthele...

We introduce a twice differentiable augmented Lagrangian for nonlinear optimization with general inequality constraints and show that strict local minimizer of the original problem is an approximate solution Lagrangian. A novel method multipliers (ALM) then presented. Our originated from generalization Hestenes-Powell Lagrangian, combination interior-point technique. It shares similar algorithm...