Primal–dual interior-point algorithms for second-order cone optimization based on kernel functions

Bai, Yanqin; Wang, Guoqiang; Roos, C.

doi:10.1016/j.na.2008.07.016

Cited by 42 publications

(42 citation statements)

References 18 publications

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“…For some of them they matched the best iteration bounds for largeupdate IPMs. They managed to extend the results in [5] to semidefinite and second order cone optimization problems [27,8]. Furthermore, the results for LO in [7], which were based on a specific eligible kernel function, were extended to P * (κ)-LCPs in Bai, Lesaja, and Roos [6], again matching the best known iteration bounds with the addition of a factor that depends affinely on κ.…”

Section: Introductionmentioning

confidence: 99%

“…The original Δx and Δs are then calculated using (8) and (9). However, they can also be obtained directly by solving the following system:…”

mentioning

confidence: 99%

“…Suppose that the current iterate (x, s) is known and is in the τ -neighborhood of the corresponding μ-center, i.e., Ψ(v) ≤ τ . Next, the value of μ is reduced by the factor 1 − θ with 0 < θ < 1, which changes the value of v according to (8) and defines a new μ-center (x(μ), s(μ)). This will likely cause the increase of the value of the barrier function above the threshold value of τ , i.e., Ψ(v) ≥ τ .…”

mentioning

confidence: 99%

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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%

“…The original Δx and Δs are then calculated using (8) and (9). However, they can also be obtained directly by solving the following system:…”

mentioning

confidence: 99%

mentioning

confidence: 99%

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

Lešaja¹,

Roos²

2010

SIAM J. Optim.

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“…SOCP has been used in filter design optimization problems and beam-former optimization problem widely, and get a good practical effect. Y. Q. Bai, M. EL GHami and C. Roos [5,6] discuss using kernel function to solve dual interior point algorithm of SOCP and linear programming problems. Basing on advantages of SOCP control, it has a great practical significance for control technology and design optimization of the walking motion in the humanoid robot.…”

Section: Introductionmentioning

confidence: 99%

Research on stabilization control method for humanoid robot

Jianming¹,

Zhong²,

Zhang³

2014

Proceedings of the 3rd International Conference on Computer Science and Service System

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Abstract-For the characteristics of humanoid robot in stability control, a method called second-order cone planning is proposed for controlling the stability of robot walking. The stability control of humanoid robot is configured to convert the second order cone to be suitable for solving the problem by derivating a variety of stability constraints of robot during the walking movement. The effectiveness of the proposed method is validated through simulation and experiments Keywords-humanoid robot; second order cone; stability constraint

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“…They also proposed the framework for analyzing the algorithm based on four conditions on the kernel function to obtain the iteration bounds of the algorithm( [4]) and generalized those methods to the general optimization. ( [6])…”

Section: Introductionmentioning

confidence: 99%

An Eligible Primal-Dual Interior-Point Method for Linear Optimization

Cho¹,

Lee²

2013

East Asian mathematical journal

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Abstract. It is well known that each kernel function defines a primaldual interior-point method(IPM). Most of polynomial-time interior-point algorithms for linear optimization(LO) are based on the logarithmic kernel function ([2, 11]). In this paper we define a new eligible kernel function and propose a new search direction and proximity function based on this function for LO problems. We show that the new algorithm has O((log p) √ n log n log n ) and O((q log p) 3 2 √ n log n ) iteration bound for large-and small-update methods, respectively. These are currently the best known complexity results.

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Primal–dual interior-point algorithms for second-order cone optimization based on kernel functions

Cited by 42 publications

References 18 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

Research on stabilization control method for humanoid robot

An Eligible Primal-Dual Interior-Point Method for Linear Optimization

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