An Interior Point Parameterized Central Path Following Algorithm for Linearly Constrained Convex Programming

Liangshao Hou; Xun Qian; Li Zhi Liao; Jie Sun

doi:10.1007/s10915-022-01765-3

An Interior Point Parameterized Central Path Following Algorithm for Linearly Constrained Convex Programming

Liangshao Hou, Xun Qian, Li Zhi Liao^*, Jie Sun

^*Corresponding author for this work

Department of Mathematics

Research output: Contribution to journal › Journal article › peer-review

Abstract

An interior point algorithm is proposed for linearly constrained convex programming following a parameterized central path, which is a generalization of the central path and requires weaker convergence conditions. The convergence and polynomial-time complexity of the proposed algorithm are proved under the assumption that the Hessian of the objective function is locally Lipschitz continuous. In addition, an initialization strategy is proposed and some numerical results are provided to show the efficiency and attractiveness of the proposed algorithm.

Original language	English
Article number	95
Number of pages	31
Journal	Journal of Scientific Computing
Volume	90
Issue number	3
Early online date	8 Feb 2022
DOIs	https://doi.org/10.1007/s10915-022-01765-3
Publication status	Published - Mar 2022

Scopus Subject Areas

Software
Theoretical Computer Science
Numerical Analysis
Engineering(all)
Computational Theory and Mathematics
Computational Mathematics
Applied Mathematics

User-Defined Keywords

Convex programming
Interior point method
Path following
Polynomial-time complexity

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10.1007/s10915-022-01765-3

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title = "An Interior Point Parameterized Central Path Following Algorithm for Linearly Constrained Convex Programming",

abstract = "An interior point algorithm is proposed for linearly constrained convex programming following a parameterized central path, which is a generalization of the central path and requires weaker convergence conditions. The convergence and polynomial-time complexity of the proposed algorithm are proved under the assumption that the Hessian of the objective function is locally Lipschitz continuous. In addition, an initialization strategy is proposed and some numerical results are provided to show the efficiency and attractiveness of the proposed algorithm.",

keywords = "Convex programming, Interior point method, Path following, Polynomial-time complexity",

author = "Liangshao Hou and Xun Qian and Liao, {Li Zhi} and Jie Sun",

note = "Funding Information: The work of L.-Z. Liao was supported in part by grants from General Research Fund (GRF) of Hong Kong. The work of J. Sun was partially supported by Australia Council Research under grant DP160102918. Publisher Copyright: {\textcopyright} 2022, The Author(s), under exclusive licence to Springer Science+Business Media, LLC, part of Springer Nature.",

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doi = "10.1007/s10915-022-01765-3",

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AU - Hou, Liangshao

AU - Qian, Xun

AU - Liao, Li Zhi

AU - Sun, Jie

N1 - Funding Information: The work of L.-Z. Liao was supported in part by grants from General Research Fund (GRF) of Hong Kong. The work of J. Sun was partially supported by Australia Council Research under grant DP160102918. Publisher Copyright: © 2022, The Author(s), under exclusive licence to Springer Science+Business Media, LLC, part of Springer Nature.

PY - 2022/3

Y1 - 2022/3

N2 - An interior point algorithm is proposed for linearly constrained convex programming following a parameterized central path, which is a generalization of the central path and requires weaker convergence conditions. The convergence and polynomial-time complexity of the proposed algorithm are proved under the assumption that the Hessian of the objective function is locally Lipschitz continuous. In addition, an initialization strategy is proposed and some numerical results are provided to show the efficiency and attractiveness of the proposed algorithm.

AB - An interior point algorithm is proposed for linearly constrained convex programming following a parameterized central path, which is a generalization of the central path and requires weaker convergence conditions. The convergence and polynomial-time complexity of the proposed algorithm are proved under the assumption that the Hessian of the objective function is locally Lipschitz continuous. In addition, an initialization strategy is proposed and some numerical results are provided to show the efficiency and attractiveness of the proposed algorithm.

KW - Convex programming

KW - Interior point method

KW - Path following

KW - Polynomial-time complexity

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DO - 10.1007/s10915-022-01765-3

M3 - Journal article

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SN - 0885-7474

VL - 90

JO - Journal of Scientific Computing

JF - Journal of Scientific Computing

IS - 3

M1 - 95

ER -

An Interior Point Parameterized Central Path Following Algorithm for Linearly Constrained Convex Programming

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