Primal-dual interior-point algorithm for semidefinite optimization based on a new kernel function with trigonometric barrier term

Kheirfam, Behrouz

doi:10.1007/s11075-012-9557-y

Cited by 33 publications

(15 citation statements)

References 20 publications

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“…Recently in [5,8] investigated new kernel functions with trigonometric barrier for LO. In [13] the author present a primal-dual interior-point algorithm for SDO based on kernel function…”

Section: Our Kernel Function and Some Of Its Propertiesmentioning

confidence: 99%

“…They established the worst case iteration bounds for large-and small-update methods, namely, O(n 3 4 log n ε ) and O( √ n log n ε ), respectively. In [6,13] the authors proposed a primal-dual interiorpoint algorithm for SDO and for P * (κ)-Linear Complementarity problems [7] based on a different kernel function with trigonometric barrier term and obtained the same iteration bounds as for LO.…”

Section: Introductionmentioning

confidence: 99%

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Primal-Dual Algorithms for Semidefinite Optimization Problems Based on Kernel-Function With Trigonometric Barrier Term

Ghami¹,

Wang²,

Steihaug³

2019

Int. J. of Appl. Math.

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In this paper we extended the results obtained for the first trigonometric kernel-function-based IPMs introduced by El Ghami et al. in [8] for LO to semidefinite optimization problems. The kernel function has a trigonometric Barrier Term. In this paper we generalize the analysis presented in the above paper for Semidefinit Optimization Problems (SDO). It is shown that the interior-point methods based on this function for large-update methods, the iteration bound is improved significantly. For small-update interior point methods the iteration bound is the best currently known bound for primal-dual interior point methods. The analysis for SDO deviates significantly from the analysis for linear optimization. Several new tools and techniques are derived in this paper.

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“…Recently in [5,8] investigated new kernel functions with trigonometric barrier for LO. In [13] the author present a primal-dual interior-point algorithm for SDO based on kernel function…”

Section: Our Kernel Function and Some Of Its Propertiesmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Primal-Dual Algorithms for Semidefinite Optimization Problems Based on Kernel-Function With Trigonometric Barrier Term

Ghami¹,

Wang²,

Steihaug³

2019

Int. J. of Appl. Math.

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“…Later on, Kheirfam in [11] suggested a new kernel function with trigonometric barrier term for SDO problems which enjoys O n 3 4 log n worst case complexity. In 2013, El Ghami [9] proposed a primal dual IPMs for P * (κ)-LCP based on a trigonometric barrier term and showed the worst case iteration complexity as O (1 + 2κ)n 3 4 log n , for large-update methods.…”

Section: Introductionmentioning

confidence: 99%

An interior-point method for $$P_*(\kappa )$$ P ∗ ( κ ) -linear complementarity problem based on a trigonometric kernel function

Hafshejani

Fatemi

Peyghami

2014

J. Appl. Math. Comput.

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Recently, El Ghami (Optim Theory Decis Mak Oper Res Appl 31:331-349, 2013) proposed a primal dual interior point method for P * (κ)-Linear Complementarity Problem (LCP) based on a trigonometric barrier term and obtained the worst case iteration complexity as O (1 + 2κ)n 3 4 log n for large-update methods. In this paper, we present a large update primal-dual interior point algorithm for P * (κ)-LCP based on a new trigonometric kernel function. By a simple analysis, we show that our algorithm based on the new kernel function enjoys the worst case O (1 + 2κ) √ n log n log n iteration bound for solving P * (κ)-LCP. This result improves the worst case iteration bound obtained by El Ghami for P * (κ)-LCP based on trigonometric kernel functions significantly.Keywords Kernel function · P * (κ)-linear complementarity problem · Primal-dual interior point methods · Large-update methods Mathematical Subject Classification (2010) 90C05 · 90C51

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“…As a result the analysis is much simpler than that in [16,17], whereas the iteration bounds are at least as good. Recently, Kheirfam in [10] introduced a trigonometric kernel function and analyzed the feasible primal-dual IPMs for SDO based on this kernel function. He showed that the primal-dual IPMs for solving SDO enjoys O(n Haseli [1] presented an interior-point algorithm for LO based on a new kernel function and obtained the best known iteration bound for large-update methods.…”

Section: Introductionmentioning

confidence: 99%

“…Lemma 9 in[10]) Let the kernel function ψ(t) be defined as in (1.1). Then, we have1 2 (t − 1) 2 ψ(t) 1 2 ψ (t) 2 .…”

mentioning

confidence: 99%

A Large-Update Feasible Interior-Point Algorithm for Convex Quadratic Semi-definite Optimization Based on a New Kernel Function

Kheirfam

Hasani

2013

J. Oper. Res. Soc. China

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Primal-dual interior-point algorithm for semidefinite optimization based on a new kernel function with trigonometric barrier term

Cited by 33 publications

References 20 publications

Primal-Dual Algorithms for Semidefinite Optimization Problems Based on Kernel-Function With Trigonometric Barrier Term

Primal-Dual Algorithms for Semidefinite Optimization Problems Based on Kernel-Function With Trigonometric Barrier Term

An interior-point method for $$P_*(\kappa )$$ P ∗ ( κ ) -linear complementarity problem based on a trigonometric kernel function

A Large-Update Feasible Interior-Point Algorithm for Convex Quadratic Semi-definite Optimization Based on a New Kernel Function

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