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

Research output: Contribution to 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 (US)
Journal	Journal of Scientific Computing
Volume	90
Issue number	3
DOIs	https://doi.org/10.1007/s10915-022-01765-3
State	Published - Feb 8 2022

ASJC Scopus subject areas

Computational Theory and Mathematics
Theoretical Computer Science
Software
General Engineering

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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.",

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

note = "KAUST Repository Item: Exported on 2022-04-26 Acknowledgements: The authors would like to thank the Associate Editor and one anonymous referee for their constructive comments and suggestions on the earlier version of this paper.",

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

language = "English (US)",

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AU - Hou, Liangshao

AU - Qian, Xun

AU - Liao, Li Zhi

AU - Sun, Jie

N1 - KAUST Repository Item: Exported on 2022-04-26 Acknowledgements: The authors would like to thank the Associate Editor and one anonymous referee for their constructive comments and suggestions on the earlier version of this paper.

PY - 2022/2/8

Y1 - 2022/2/8

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.

UR - http://hdl.handle.net/10754/676538

UR - https://link.springer.com/10.1007/s10915-022-01765-3

UR - http://www.scopus.com/inward/record.url?scp=85124460907&partnerID=8YFLogxK

U2 - 10.1007/s10915-022-01765-3

DO - 10.1007/s10915-022-01765-3

M3 - Article

SN - 1573-7691

VL - 90

JO - Journal of Scientific Computing

JF - Journal of Scientific Computing

IS - 3

ER -

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

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