This paper proposes an infeasible interior-point algorithm for the convex optimization problem using arc-search techniques. The proposed simultaneously selects centering parameter and step size, aiming at optimizing performance in every iteration. Analytic formulas are provided to make method very efficient. convergence of is proved a polynomial bound established. preliminary numerical test res...

This paper studies a new potential-function and an infeasible-interior-point method based on this function for the solution of linear programming problems. This work is motivated by the apparent gap between the algorithms with the best worst-case complexity and their most successful implementations. For example, analyses of the algorithms are usually carried out by imposing several regularity a...

We propose a new infeasible path-following algorithm for convex linearlyconstrained quadratic programming problem. This algorithm utilizes the monomial method rather than Newton's method for solving the KKT equations at each iteration. As a result, the sequence of iterates generated by this new algorithm is infeasible in the primal and dual linear constraints, but, unlike the sequence of iterat...

In this paper, we introduce the truncated primal-infeasible dual-feasible interior point algorithm for linear programming and describe an implementation of this algorithm for solving the minimum cost network flow problem. In each iteration, the linear system that determines the search direction is computed inexactly, and the norm of the resulting residual vector is used in the stopping criteria...

We use the globally convergent framework proposed by Kojima, Noma, and Yoshise to construct an infeasible-interior-point algorithm for monotone nonlinear complemen-tarity problems. Superlinear convergence is attained when the solution is nondegener-ate and also when the problem is linear. Numerical experiments connrm the eecacy of the proposed approach.

Multistage stochastic linear programming (MSLP) is a powerful tool for making decisions under uncertainty. A deteministic equivalent of MSLP is a large-scale linear program with nonanticipativity constraints. Recently developed infeasible interior point methods are used to solve the resulting linear program. Technical problems arising from this approach include rank reduction and computation of...

We present a modified version of the infeasible-interiorpoint algorithm for monotone linear complementary problems introduced 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 different feasibility step, which targets at the μ-center. It results a better iteration bound.

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 discuss a polynomial and Q-subquadratically convergent algorithm for linear complementarity problems that does not require feasibility of the initial point or the subsequent iterates. The algorithm is a modiication of the linearly convergent method of Zhang and requires the solution of at most two linear systems with the same coeecient matrix at each iteration.

We consider a modiication of a path-following infeasible-interior-point algorithm described by Wright. In the new algorithm, we attempt to improve each major iterate by reusing the coeecient matrix factors from the latest step. We show that the modiied algorithm has similar theoretical global convergence properties to those of the earlier algorithm, while its asymptotic convergence rate can be ...