An infeasible-start path-following method for monotone LCPs

Zhang, Pei-ai; Li, Xingsi

doi:10.1016/s0895-7177(03)90003-3

Cited by 3 publications

(13 citation statements)

References 9 publications

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“…Various IPMs for LO have been successfully generalized to LCPs. Besides the aforementioned monograph of Kojima et al [13], and without any attempt to be complete, we mention a few other relevant references: [2,17,18,28,29,30].…”

Section: Introductionmentioning

confidence: 99%

Unified Analysis of Kernel-Based Interior-Point Methods for $P_*(\kappa)$-Linear Complementarity Problems

Lešaja¹,

Roos²

2010

SIAM J. Optim.

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Abstract. We present an interior-point method for the P * (κ)-linear complementarity problem (LCP) that is based on barrier functions which are defined by a large class of univariate functions called eligible kernel functions. This class is fairly general and includes the classical logarithmic function and the self-regular functions, as well as many non-self-regular functions as special cases. We provide a unified analysis of the method and give a general scheme on how to calculate the iteration bounds for the entire class. We also calculate the iteration bounds of both long-step and short-step versions of the method for several specific eligible kernel functions. For some of them we match the best known iteration bounds for the long-step method, while for the short-step method the iteration bounds are of the same order of magnitude. As far as we know, this is the first paper that provides a unified approach and comprehensive treatment of interior-point methods for P * (κ)-LCPs based on the entire class of eligible kernel functions.

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Section: Introductionmentioning

confidence: 99%

Unified Analysis of Kernel-Based Interior-Point Methods for $P_*(\kappa)$-Linear Complementarity Problems

Lešaja¹,

Roos²

2010

SIAM J. Optim.

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“…This definition generalizes and unifies the search directions proposed in [35] (η = 1) and [37] (η = 1 σ with σ ∈ (0.5, 1) and σ < min 1, ln 1…”

Section: Entropy Based Search Directions and Basic Propertiesmentioning

confidence: 57%

“…In the vast literature on primal-dual interior-point methods, two of the closest treatments to ours are [35] and [37]. Our search directions unify and generalize the search directions introduced in [35] and [37].…”

Section: Introductionmentioning

confidence: 92%

“…. These search directions have been studied in [37] in the wide neighborhood for the special case that η = 1 σ with σ ∈ (0.5, 1) and σ < min 1, ln 1 1−β . In this paper, we study these search directions for a wider range of η.…”

Section: Algorithm For the Wide Neighborhoodsmentioning

confidence: 99%

“…For example, the choice of f (x) = 1/x gives the search direction proposed in [24] (also see [25] for another connection to the entropy function), and the choice of f (x) = √ x leads to the work in [6]. A natural choice for f is ln(•), which has been studied in [35], [37], and [28]. Substituting f (x) = ln(x) in (3) results in…”

Section: Introductionmentioning

confidence: 99%

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Primal-dual entropy-based interior-point algorithms for linear optimization

Karimi

Luo²,

Tunçel

2017

RAIRO-Oper. Res.

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We propose a family of search directions based on primal-dual entropy in the context of interior-point methods for linear optimization. We show that by using entropy based search directions in the predictor step of a predictor-corrector algorithm together with a homogeneous self-dual embedding, we can achieve the current best iteration complexity bound for linear optimization. Then, we focus on some wide neighborhood algorithms and show that in our family of entropy based search directions, we can find the best search direction and step size combination by performing a plane search at each iteration. For this purpose, we propose a heuristic plane search algorithm as well as an exact one. Finally, we perform computational experiments to study the performance of entropy-based search directions in wide neighborhoods of the central path, with and without utilizing the plane search algorithms.

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Mehrotra-type predictor–corrector algorithms for sufficient linear complementarity problem

Liu

2012

Applied Numerical Mathematics

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An infeasible-start path-following method for monotone LCPs

Cited by 3 publications

References 9 publications

Unified Analysis of Kernel-Based Interior-Point Methods for $P_*(\kappa)$-Linear Complementarity Problems

Unified Analysis of Kernel-Based Interior-Point Methods for $P_*(\kappa)$-Linear Complementarity Problems

Primal-dual entropy-based interior-point algorithms for linear optimization

Mehrotra-type predictor–corrector algorithms for sufficient linear complementarity problem

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