Generalized affine scaling trajectory analysis for linearly constrained convex programming

Xun Qian; Lizhi Liao

doi:10.1007/978-3-319-92537-0_17

Generalized affine scaling trajectory analysis for linearly constrained convex programming

Xun Qian
, Lizhi Liao^*

^*Corresponding author for this work

Department of Mathematics

Research output: Chapter in book/report/conference proceeding › Conference proceeding › peer-review

1 Citation (Scopus)

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.

Original language	English
Title of host publication	Advances in Neural Networks – ISNN 2018
Subtitle of host publication	15th International Symposium on Neural Networks, ISNN 2018, Minsk, Belarus, June 25–28, 2018, Proceedings
Editors	Changyin Sun, Alexander V. Tuzikov, Tingwen Huang, Jiancheng Lv
Publisher	Springer Cham
Pages	139-147
Number of pages	9
Edition	1st
ISBN (Electronic)	9783319925370
ISBN (Print)	9783319925363
DOIs	https://doi.org/10.1007/978-3-319-92537-0_17
Publication status	Published - 25 May 2018
Event	15th International Symposium on Neural Networks, ISNN 2018 - Minsk, Belarus Duration: 25 Jun 2018 → 28 Jun 2018

Publication series

Name	Lecture Notes in Computer Science
Volume	10878
ISSN (Print)	0302-9743
ISSN (Electronic)	1611-3349

Name	Theoretical Computer Science and General Issues
ISSN (Print)	2512-2010
ISSN (Electronic)	2512-2029

Name	ISNN: International Symposium on Neural Networks

Conference

Conference	15th International Symposium on Neural Networks, ISNN 2018
Country/Territory	Belarus
City	Minsk
Period	25/06/18 → 28/06/18

User-Defined Keywords

Continuous trajectory
Convex programming
Interior point method
Ordinary differential equation

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10.1007/978-3-319-92537-0_17

Cite this

Qian, X., & Liao, L. (2018). Generalized affine scaling trajectory analysis for linearly constrained convex programming. In C. Sun, A. V. Tuzikov, T. Huang, & J. Lv (Eds.), Advances in Neural Networks – ISNN 2018: 15th International Symposium on Neural Networks, ISNN 2018, Minsk, Belarus, June 25–28, 2018, Proceedings (1st ed., pp. 139-147). (Lecture Notes in Computer Science; Vol. 10878), (Theoretical Computer Science and General Issues), (ISNN: International Symposium on Neural Networks). Springer Cham. https://doi.org/10.1007/978-3-319-92537-0_17

Qian, Xun ; Liao, Lizhi. / Generalized affine scaling trajectory analysis for linearly constrained convex programming. Advances in Neural Networks – ISNN 2018: 15th International Symposium on Neural Networks, ISNN 2018, Minsk, Belarus, June 25–28, 2018, Proceedings. editor / Changyin Sun ; Alexander V. Tuzikov ; Tingwen Huang ; Jiancheng Lv. 1st. ed. Springer Cham, 2018. pp. 139-147 (Lecture Notes in Computer Science). (Theoretical Computer Science and General Issues). (ISNN: International Symposium on Neural Networks).

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title = "Generalized affine scaling trajectory analysis for linearly constrained convex programming",

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",

author = "Xun Qian and Lizhi Liao",

note = "Publisher Copyright: {\textcopyright} Springer International Publishing AG, part of Springer Nature 2018.; 15th International Symposium on Neural Networks, ISNN 2018 ; Conference date: 25-06-2018 Through 28-06-2018",

year = "2018",

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Qian, X & Liao, L 2018, Generalized affine scaling trajectory analysis for linearly constrained convex programming. in C Sun, AV Tuzikov, T Huang & J Lv (eds), Advances in Neural Networks – ISNN 2018: 15th International Symposium on Neural Networks, ISNN 2018, Minsk, Belarus, June 25–28, 2018, Proceedings. 1st edn, Lecture Notes in Computer Science, vol. 10878, Theoretical Computer Science and General Issues, ISNN: International Symposium on Neural Networks, Springer Cham, pp. 139-147, 15th International Symposium on Neural Networks, ISNN 2018, Minsk, Belarus, 25/06/18. https://doi.org/10.1007/978-3-319-92537-0_17

Generalized affine scaling trajectory analysis for linearly constrained convex programming. / Qian, Xun; Liao, Lizhi.
Advances in Neural Networks – ISNN 2018: 15th International Symposium on Neural Networks, ISNN 2018, Minsk, Belarus, June 25–28, 2018, Proceedings. ed. / Changyin Sun; Alexander V. Tuzikov; Tingwen Huang; Jiancheng Lv. 1st. ed. Springer Cham, 2018. p. 139-147 (Lecture Notes in Computer Science; Vol. 10878), (Theoretical Computer Science and General Issues), (ISNN: International Symposium on Neural Networks).

Research output: Chapter in book/report/conference proceeding › Conference proceeding › peer-review

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PY - 2018/5/25

Y1 - 2018/5/25

N2 - 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.

AB - 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.

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Qian X, Liao L. Generalized affine scaling trajectory analysis for linearly constrained convex programming. In Sun C, Tuzikov AV, Huang T, Lv J, editors, Advances in Neural Networks – ISNN 2018: 15th International Symposium on Neural Networks, ISNN 2018, Minsk, Belarus, June 25–28, 2018, Proceedings. 1st ed. Springer Cham. 2018. p. 139-147. (Lecture Notes in Computer Science). (Theoretical Computer Science and General Issues). (ISNN: International Symposium on Neural Networks). doi: 10.1007/978-3-319-92537-0_17

Generalized affine scaling trajectory analysis for linearly constrained convex programming

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