A new interior-point algorithm based on modified Nesterov–Todd direction for symmetric cone linear complementarity problem

Kheirfam, Behrouz; Mahdavi–Amiri, Nezam

doi:10.1007/s11590-013-0618-5

Cited by 18 publications

(14 citation statements)

References 19 publications

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“…where the first inequality and the third equality are respectively true by Lemma 2.4 and the second equation of (5) and the last inequality follows by the triangle inequality and Lemma 13 in [9].…”

Section: Definingmentioning

confidence: 97%

“…Here, we briefly recall the concepts of the central path, modified NT-directions for SCLCP, recently given by Kheirfam and Mahdavi-Amiri [9]. Consider the monotone SCLCP in the standard form: Given an n-dimensional Euclidean Jordan algebra (J , •, ., . )…”

Section: Modified Full Nt-stepmentioning

confidence: 99%

“…Lesaja and Roos [8] presented an IPM for SCLCP that is based on barrier functions which are defined by a large class of univariate functions, called eligible kernel functions. Kheirfam and Mahdavi-Amiri [9] also introduced a new interior-point algorithm for SCLCP by modifying the Nesterov-Todd (NT) step. The authors proved that the algorithm stops after at most O( √ r log r μ 0 ) iterations, being in accord with the best existing bound for IPMs.…”

Section: Introductionmentioning

confidence: 99%

“…Inspired by the above-mentioned works, in particular [9,15], here we propose a full NT-step infeasible interior-point algorithm for SCLCP based on modified NT directions. Compared with other IIPMs, the ideas underlying our proposed algorithm, based on modified NT directions, are quite simple and the associated analysis turns to be elegant.…”

Section: Introductionmentioning

confidence: 99%

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An infeasible interior-point algorithm based on modified Nesterov and Todd directions for symmetric linear complementarity problem

Kheirfam

Mahdavi–Amiri

2014

Optimization

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We present an infeasible interior-point algorithm for symmetric linear complementarity problem based on modified Nesterov-Todd directions by using Euclidean Jordan algebras. The algorithm decreases the duality gap and the feasibility residual at the same rate. In this algorithm, we construct strictly feasible iterates for a sequence of perturbations of the given problem. Each main iteration of the algorithm consists of a feasibility step and a number of centring steps. The starting point in the first iteration is strictly feasible for a perturbed problem. The feasibility steps lead to a strictly feasible iterate for the next perturbed problem. By using centring steps for the new perturbed problem, a strictly feasible iterate is obtained to be close to the central path of the new perturbed problem. Furthermore, giving a complexity analysis of the algorithm, we derive the currently best-known iteration bound for infeasible interior-point methods.

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Section: Definingmentioning

confidence: 97%

Section: Modified Full Nt-stepmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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An infeasible interior-point algorithm based on modified Nesterov and Todd directions for symmetric linear complementarity problem

Kheirfam

Mahdavi–Amiri

2014

Optimization

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“…Kheirfam introduced an infeasible IPM for SCO in [13]. Kheirfam and Mahdavi-Amiri [14] and Kheirfam [15] presented a new full-Newton step interior-point algorithm for SCO and the Cartesian P * (κ)-LCP over symmetric cones based on modified Newton direction which differs from Darvay's search direction only by a constant multiplier, respectively. Furthermore, Wang proposed a new polynomial interior-point algorithm for the monotone LCPs over symmetric cones with full Nesterov-Todd step [25].…”

Section: Introductionmentioning

confidence: 99%

A full-Newton step feasible interior-point algorithm for P∗(κ)-LCP based on a new search direction

Kheirfam¹,

Haghighi²

2016

CRORR

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Abstract. In this paper, we present a full-Newton step feasible interior-point algorithm for a P * (κ) linear complementarity problem based on a new search direction. We apply a vector-valued function generated by a univariate function on nonlinear equations of the system which defines the central path. Furthermore, we derive the iteration bound for the algorithm, which coincides with the best-known iteration bound for these types of algorithms. Numerical results show that the proposed algorithm is competitive and reliable.

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Simplified Full-Newton Step Method with a Kernel Function

Hong-mei

Gao

Zhao

2022

Advanced Intelligent Technologies for Industry

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A new interior-point algorithm based on modified Nesterov–Todd direction for symmetric cone linear complementarity problem

Cited by 18 publications

References 19 publications

An infeasible interior-point algorithm based on modified Nesterov and Todd directions for symmetric linear complementarity problem

An infeasible interior-point algorithm based on modified Nesterov and Todd directions for symmetric linear complementarity problem

A full-Newton step feasible interior-point algorithm for P∗(κ)-LCP based on a new search direction

Simplified Full-Newton Step Method with a Kernel Function

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