Generalized affine scaling trajectory analysis for linearly constrained convex programming

Xun Qian, Lizhi LIAO*

*Corresponding author for this work

Research output: Chapter in book/report/conference proceedingConference proceedingpeer-review

1 Citation (Scopus)


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.

Original languageEnglish
Title of host publicationAdvances in Neural Networks - ISNN 2018 - 15th International Symposium on Neural Networks, ISNN 2018, Proceedings
EditorsChangyin Sun, Alexander V. Tuzikov, Tingwen Huang, Jiancheng Lv
PublisherSpringer Verlag
Number of pages9
ISBN (Print)9783319925363
Publication statusPublished - 2018
Event15th International Symposium on Neural Networks, ISNN 2018 - Minsk, Belarus
Duration: 25 Jun 201828 Jun 2018

Publication series

NameLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume10878 LNCS
ISSN (Print)0302-9743
ISSN (Electronic)1611-3349


Conference15th International Symposium on Neural Networks, ISNN 2018

Scopus Subject Areas

  • Theoretical Computer Science
  • Computer Science(all)

User-Defined Keywords

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


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