Singularly perturbed nonlinear ODEs and interior point optimization algorithms

Author

Ezzine, Jelel ; Ben-Daya, M.

Author_Institution

Dept. of Syst. Eng., King Fahd Univ. of Pet. & Miner., Dhahran, Saudi Arabia

Volume

3

fYear

1995

fDate

21-23 Jun 1995

Firstpage

1816

Abstract

This paper explores the continuous realizations of iterative processes emanating from interior point optimization algorithms, and their connection with nonlinear singularly-perturbed ordinary differential equations. This mathematical connection provides a theoretical framework for the analysis of the dynamical properties long known and exploited in interior point-based optimization techniques. In addition, this connection is used to show that the logarithmic barrier function is indeed, in some sense, optimum

Keywords

Newton method; dynamics; linear programming; nonlinear differential equations; perturbation techniques; Newton method; discrete dynamics; interior point optimization; iterative processes; linear programming; logarithmic barrier function; nonlinear differential equations; singularly-perturbed ordinary differential equations; Differential equations; Iterative methods; Large-scale systems; Linear programming; Newton method; Petroleum; Polynomials; Region 2; Stress; Systems engineering and theory;

fLanguage

English

Publisher

ieee

Conference_Titel

American Control Conference, Proceedings of the 1995

Conference_Location

Seattle, WA

Print_ISBN

0-7803-2445-5

Type

conf

DOI

10.1109/ACC.1995.531198

Filename

531198