Some Jordan algebras were proved more than a decade ago to be an indispensable tool in the unified study of interior-point methods. By using it, we generalize the infeasible interiorpoint method for linear optimization of Roos [SIAM J. Optim., 16(4):1110–1136 (electronic), 2006] to symmetric optimization. This unifies the analysis for linear, second-order cone and semidefinite optimizations.

In this paper we generalize an infeasible interior-point method for linear optimization to horizontal linear complementarity problem (HLCP). This algorithm starts from strictly feasible iterates on the central path of a perturbed problem that is produced by suitable perturbation in HLCP problem. Then, we use so-called feasibility steps that serves to generate strictly feasible iterates for the ...

In this paper we analyze the rate of local convergence of the Newton primal-dual interiorpoint method when the iterates are kept strictly feasible with respect to the inequality constraints. It is shown under the classical conditions that the rate is q–quadratic when the functions associated to the binding inequality constraints are concave. In general, the q–quadratic rate is achieved provided...

This paper proposes a globally convergent predictor-corrector infeasible-interiorpoint algorithm for the monotone semide nite linear complementarity problem using the AlizadehHaeberly-Overton search direction, and shows its quadratic local convergence under the strict complementarity condition.

Recently, Roos proposed a full-Newton step infeasible interiorpoint method (IIPM) for solving linear optimization (LO) problems. Later on, more variants of this algorithm were published. However, each main step of these methods is composed of one feasibility step and several centering steps. The purpose of this paper is to prove that by using a new search direction it is enough to take only one...

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 propose a family of directions that generalizes many directions proposed so far in interiorpoint methods for the SDP (semide nite programming) and for the monotone SDLCP (semide nite linear complementarity problem). We derive the family from the Helmberg-Rendl-Vanderbei-Wolkowicz/KojimaShindoh-Hara/Monteiro direction by relaxing its \centrality equation" into a \centrality inequality." Using...

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 ...

We describe an optimization method for large-scale nonnegative regularization. The method is an interiorpoint iteration that requires the solution of a large-scale and possibly ill-conditioned parameterized trust-region subproblem at each step. The method relies on recently developed techniques for the large-scale trust-region subproblem. We present preliminary numerical results on image restor...

In this study, we implement a variant of infeasible interior-point algorithm for solving monotone linear complementarity problems (LCP). We first reformulate the LCP as an minimization problem. Then descent iterative method is applied to latter. The direction computed via Newton method. However, maintaining positivity iterates, novel and efficient strategy proposed. Some numerical results are r...