After a brief introduction to Jordan algebras, we present a primal-dual interior-point algorithm for second-order conic optimization that uses full Nesterov-Todd-steps; no line searches are required. The number of iterations of the algorithm is O( √ N log(N/ε), where N stands for the number of second-order cones in the problem formulation and ε is the desired accuracy. The bound coincides with ...

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...

Based on extensive computational evidence (hundreds of thousands of randomly generated problems) the second author conjectured that κ̄(ζ) = 1 (Conjecture 5.1 in [1]), which is a factor of √ 2n better than has been proved in [1], and which would yield an O( √ n) iteration full-Newton step infeasible interior-point algorithm. In this paper we present an example showing that κ̄(ζ) is in the order of...

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.

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.

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.

An approach to determine primal and dual stepsizes in the infeasible{ interior{point primal{dual method for convex quadratic problems is presented. The approach reduces the primal and dual infeasibilities in each step and allows diierent stepsizes. The method is derived by investigating the eecient set of a multiobjective optimization problem. Computational results are also given.

We present an infeasible-interior-point algorithm for monotone linear complementarity problems in which the search directions are affine scaling directions and the step lengths are obtained from simple formulae that ensure both global and superlinear convergence. By choosing the value of a parameter in appropriate ways, polynomial complexity and convergence with Q-order up to (but not including...