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International Symposium on Neural Networks

ISNN 2018: Advances in Neural Networks – ISNN 2018 pp 139–147Cite as

Generalized Affine Scaling Trajectory Analysis for Linearly Constrained Convex Programming

Part of the Lecture Notes in Computer Science book series (LNTCS,volume 10878)

Abstract

In this paper, we propose and analyze a continuous trajectory, which is the solution of an ordinary differential equation (ODE) system for solving linearly constrained convex programming. The ODE system is formulated based on a first-order interior point method in [Math. Program., 127, 399–424 (2011)] which combines and extends a first-order affine scaling method and the replicator dynamics method for quadratic programming. The solution of the corresponding ODE system is called the generalized affine scaling trajectory. By only assuming the existence of a finite optimal solution, we show that, starting from any interior feasible point, (i) the continuous trajectory is convergent; and (ii) the limit point is indeed an optimal solution of the original problem.

Keywords

  • Continuous trajectory
  • Convex programming
  • Interior point method
  • Ordinary differential equation

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Author information

Authors and Affiliations

  1. Department of Mathematics, Hong Kong Baptist University, Kowloon Tong, Kowloon, Hong Kong, PRC

    Xun Qian & Li-Zhi Liao

Authors
  1. Xun Qian
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  2. Li-Zhi Liao
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Correspondence to Li-Zhi Liao .

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Editors and Affiliations

  1. Texas A&M University at Qatar, Doha, Qatar

    Tingwen Huang

  2. Sichuan University, Chengdu, China

    Jiancheng Lv

  3. Southeast University, Nanjing, China

    Changyin Sun

  4. United Institute of Informatics Problems, Minsk, Belarus

    Alexander V. Tuzikov

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Qian, X., Liao, LZ. (2018). Generalized Affine Scaling Trajectory Analysis for Linearly Constrained Convex Programming. In: Huang, T., Lv, J., Sun, C., Tuzikov, A. (eds) Advances in Neural Networks – ISNN 2018. ISNN 2018. Lecture Notes in Computer Science(), vol 10878. Springer, Cham. https://doi.org/10.1007/978-3-319-92537-0_17

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  • DOI: https://doi.org/10.1007/978-3-319-92537-0_17

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-92536-3

  • Online ISBN: 978-3-319-92537-0

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