A full Nesterov-Todd step infeasible interior-point algorithm for symmetric cone linear complementarity problem

Authors

Abstract:

‎A full Nesterov-Todd (NT) step infeasible interior-point algorithm‎ ‎is proposed for solving monotone linear complementarity problems‎ ‎over symmetric cones by using Euclidean Jordan algebra‎. ‎Two types of‎ ‎full NT-steps are used‎, ‎feasibility steps and centering steps‎. ‎The‎ ‎algorithm starts from strictly feasible iterates of a perturbed‎ ‎problem‎, ‎and, using the central path and feasibility steps, find‎s ‎strictly feasible iterates for the next perturbed problem‎. ‎By using‎ ‎centering steps for the new perturbed problem‎, ‎strictly feasible‎ ‎iterates are obtained to be close enough to the central path of the‎ ‎new perturbed problem‎. ‎The starting point depends on two positive‎ ‎numbers $rho_p$ and $rho_d$‎. ‎The algorithm terminates either by‎ ‎finding an $epsilon$-solution or detecting that the symmetric cone ‎linear complementarity problem has no optimal solution with‎ ‎vanishing duality gap satisfying a condition in terms of $rho_p$‎ ‎and $rho_d$‎. ‎The iteration bound coincides with the best known‎ ‎bound for infeasible interior-point methods‎.

Upgrade to premium to download articles

Sign up to access the full text

Already have an account?login

similar resources

a full nesterov-todd step infeasible interior-point algorithm for symmetric cone linear complementarity problem

‎a full nesterov-todd (nt) step infeasible interior-point algorithm‎ ‎is proposed for solving monotone linear complementarity problems‎ ‎over symmetric cones by using euclidean jordan algebra‎. ‎two types of‎ ‎full nt-steps are used‎, ‎feasibility steps and centering steps‎. ‎the‎ ‎algorithm starts from strictly feasible iterates of a perturbed‎ ‎problem‎, ‎and, using the central path and feasi...

full text

A Full Nesterov-todd Step Infeasible Interior-point Algorithm for Symmetric Cone Linear Complementarity Problem

A full Nesterov-Todd (NT) step infeasible interior-point algorithm is proposed for solving monotone linear complementarity problems over symmetric cones by using Euclidean Jordan algebra. Two types of full NT-steps are used, feasibility steps and centering steps. The algorithm starts from strictly feasible iterates of a perturbed problem, and, using the central path and feasibility steps, finds...

full text

A New Infeasible Interior-Point Algorithm with Full Nesterov-Todd Step for Semi-Definite Optimization

  We present a new full Nesterov and Todd step infeasible interior-point algorithm for semi-definite optimization. The algorithm decreases the duality gap and the feasibility residuals at the same rate. In the algorithm, we construct strictly feasible iterates for a sequence of perturbations of the given problem and its dual problem. Every main iteration of the algorithm consists of a feasibili...

full text

A Full-NT Step Infeasible Interior-Point Algorithm for Mixed Symmetric Cone LCPs

An infeasible interior-point algorithm for mixed symmetric cone linear complementarity problems is proposed. Using the machinery of Euclidean Jordan algebras and Nesterov-Todd search direction, the convergence analysis of the algorithm is shown and proved. Moreover, we obtain a polynomial time complexity bound which matches the currently best known iteration bound for infeasible interior-point ...

full text

An infeasible interior-point algorithm with full Nesterov-Todd step for second-order cone programming

This paper proposes an infeasible interior-point algorithm with full Nesterov-Todd step for second-order cone programming, which is an extension of the work of Roos (SIAM J. Optim., 16(4):1110–1136, 2006). The polynomial bound coincides with that of infeasible interior-point methods for linear programming, namely, O(l log l/ε).

full text

Full Nesterov-todd Step Interior-point Methods for Symmetric Optimization

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.

full text

My Resources

Save resource for easier access later

Save to my library Already added to my library

{@ msg_add @}


Journal title

volume 40  issue 3

pages  541- 564

publication date 2014-06-01

By following a journal you will be notified via email when a new issue of this journal is published.

Hosted on Doprax cloud platform doprax.com

copyright © 2015-2023