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ANALYSIS OF A SMOOTHING METHOD FOR symmetric conic linear programming

JOURNAL OF APPLIED MATHEMATICS AND COMPUTING 2006年第1-2期22卷 133-148页

作者： Liu, Yong-Jin Zhang, Li-Wei Wang, Yin-He Shantou Univ Dept Math Shantou 515063 Peoples R China Dalian Univ Technol Dept Math Dalian Peoples R China

This paper proposes a smoothing method for symmetric conic linear programming (SCLP). We first characterize the central path conditions for SCLP problems with the help of Chen-Harker-Kanzow-Smale smoothing function. A smoothing-type algorithm is constructed based on this characterization and the global convergence and locally quadratic convergence for the proposed algorithm are demonstrated.

关键词： symmetric conic linear programming smoothing methods global convergence locally quadratic convergence

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A Globally Convergent Smoothing Method for symmetric conic linear programming

A Globally Convergent Smoothing Method for Symmetric Conic L...

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4th International Symposium on Intelligence Computation and Applications

作者： Chi, Xiaoni Li, Ping Huanggang Normal Univ Coll Math & Informat Sci Huangzhou 438000 Hubei Peoples R China

ISBN: (纸本)9783642048425

Based on the Chen-Harker-Kanzow-Smale smoothing function, a smoothing Newton method is developed for solving the symmetric conic linear programming. Without any restrictions for its starting point, this algorithm solves only one linear system of equations at each iteration and proves to be Globally convergent in absence of uniform nonsingularity. Numerical results indicate that it is promising in future applications.

关键词： symmetric conic linear programming smoothing method Chen-Harker-Kanzow-Smale smoothing function global convergence

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A Novel Smoothing Method for symmetric conic linear programming

A Novel Smoothing Method for Symmetric Conic Linear Programm...

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International Conference on Computing, Information and Control (ICCIC 2011)

作者： Chi, Xiaoni Liu, June Huanggang Normal Univ Coll Math & Informat Sci Huanggang 438000 Hubei Peoples R China

ISBN: (纸本)9783642239922

We present a novel smoothing method for solving the symmetric conic linear programming based on the Chen-Harker-Kanzow-Smale (CHKS) smoothing function. Unlike interior point methods, the proposed algorithm can start from an arbitrary point. Our algorithm solves only one linear system of equations and performs only one line search at each iteration. Without uniform nonsingularity, the proposed algorithm is shown to be globally convergent. Numerical results indicate that our algorithm is promising.

关键词： symmetric conic linear programming smoothing method Chen-Harker-Kanzow-Smale smoothing function global convergence

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A Novel Smoothing Method for symmetric conic linear programming

A Novel Smoothing Method for Symmetric Conic Linear Programm...

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2010 Second International Seminar On Business and Information Management (ISBIM 2010)

作者： Xiaoni Chi , June Liu College of Mathematics and Information Science Huanggang Normal University Huanggang 438000, Hubei, P.R. China

关键词： symmetric conic linear programming smoothing method Chen-Harker-Kanzow-Smale smoothing function global convergence

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A Novel Smoothing Method for symmetric conic linear programming

A Novel Smoothing Method for Symmetric Conic Linear Programm...

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The 2011 International Conference on Computing,Information and Control(ICCIC 2011)

作者： Xiaoni Chi June Liu College of Mathematics and Information Science Huanggang Normal University

We present a novel smoothing method for solving the symmetric conic linear programming based on the Chen-Harker-Kanzow-Smale(CHKS) smoothing function. Unlike interior point methods, the proposed algorithm can start from an arbitrary point. Our algorithm solves only one linear system of equations and performs only one line search at each iteration. Without uniform nonsingularity, the proposed algorithm is shown to be globally convergent. Numerical results indicate that our algorithm is promising.

关键词： symmetric conic linear programming smoothing method ChenHarker-Kanzow-Smale smoothing function global convergence

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A New Inexact Smoothing Method for SCLP

A New Inexact Smoothing Method for SCLP

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2013 4th International Conference on Information Technology for Manufacturing Systems(ITMS 2013)

作者： Xiaoni Chi Qing Zhang College of Mathematics and Computer Science Huanggang Normal University School of Mathematics and Statistics Wuhan University

In this paper, a new inexact smoothing method is presented for solving the symmetric conic linear programming(SCLP) in materials. Based on a regularized version of Chen-Harker-Kanzow-Smale smoothing function, our algorithm reformulates the SCLP as an equivalent nonlinear system of equations. At each iteration, Newton's method is adopted to solve the system approximately. Under suitable assumptions, the algorithm is proved to possess global convergence and local superlinear convergence.

关键词： symmetric conic linear programming Smoothing Newton method Inexact search direction Global convergence

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