A new infeasible interior-point method based on Darvay’s technique for symmetric optimization

Kheirfam, Behrouz

doi:10.1007/s10479-013-1474-5

Cited by 20 publications

(9 citation statements)

References 16 publications

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“…In [13,15] the transformation is achieved by the square root function. Since then, this technique has been extended to different types of optimization problems, for LCP [1,3,5,6,34,39,44,46], for convex quadratic programming (CQP) [2], for semidefinite programing (SDP) [7,45], for second-order cone programming (SOCP) [46] and symmetric optimization (SO) [33,47].…”

Section: Introductionmentioning

confidence: 99%

Interior-point algorithm for sufficient LCPs based on the technique of algebraically equivalent transformation

2020

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We present a short-step interior-point algorithm (IPA) for sufficient linear complementarity problems (LCPs) based on a new search direction. An algebraic equivalent transformation (AET) is used on the centrality equation of the central path system and Newton’s method is applied on this modified system. This technique was offered by Zsolt Darvay for linear optimization in 2002. Darvay first used the square root function as AET and in 2012 Darvay et al. applied this technique with an other transformation formed by the difference of the identity map and the square root function. We apply the AET technique with the new function to transform the central path equation of the sufficient LCPs. This technique leads to new search directions for the problem. We introduce an IPA with full Newton steps and prove that the iteration bound of the algorithm coincides with the best known one for sufficient LCPs. We present some numerical results to illustrate performance of the proposed IPA on two significantly different sets of test problems and compare it, with related, quite similar variants of IPAs.

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Section: Introductionmentioning

confidence: 99%

Interior-point algorithm for sufficient LCPs based on the technique of algebraically equivalent transformation

2020

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“…Later on, Achache [1], Wang and Bai [27,28,29] and Wang et al [30] extended Darvay's algorithm for LO to convex quadratic optimization (CQO), semidefinite optimization (SDO), second-order cone optimization (SOCO), symmetric cone optimization (SCO) and P * (κ)-LCP, respectively. 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.…”

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

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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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“…Wang and Bai [19,20] extended Darvay's interior-point algorithm for LO to SOCO and SCO with a full Nesterov-Todd (NT) step, respectively. Ahmadi et al [1] and Kheirfam [9] adapted Darvay's technique to IIPMs for LO and SCO, respectively. All IIPMs mentioned so far consist of one feasibility step and a few (at most three) centering steps.…”

Section: Introductionmentioning

confidence: 99%

A New Infeasible Interior-Point Method Based on a Non-Coercive Kernel Function with Improved Centering Steps for Second-Order Cone Optimization

Kheirfam

2015

Numerical Functional Analysis and Optimization

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In this article, we present a new full Nesterov-Todd step infeasible interior-point method for second-order cone optimization based on a non-coercive kernel function. The main iteration consists of a so-called feasibility step and one centering step, whereas the earlier versions, in [4,21], needed two additional centering steps. We use a kernel function to induce the feasibility step. The new algorithm reduces the searching steps in each iteration and tenders an interesting analysis for complexity bound.

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A new infeasible interior-point method based on Darvay’s technique for symmetric optimization

Cited by 20 publications

References 16 publications

Interior-point algorithm for sufficient LCPs based on the technique of algebraically equivalent transformation

Interior-point algorithm for sufficient LCPs based on the technique of algebraically equivalent transformation

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

A New Infeasible Interior-Point Method Based on a Non-Coercive Kernel Function with Improved Centering Steps for Second-Order Cone Optimization

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