Skip to main content
U.S. flag

An official website of the United States government

Official websites use .gov
A .gov website belongs to an official government organization in the United States.

Secure .gov websites use HTTPS
A lock ( ) or https:// means you’ve safely connected to the .gov website. Share sensitive information only on official, secure websites.

Logarithmic SUMT Limits in Convex Programming

Published

Author(s)

G P. McCormick, Christoph J. Witzgall

Abstract

The limits of a class of primal and dual solution trajectories associated with the Sequential Unconstrained Minimization Technique (SUMT) are investigated for convex programming problems with non-unique optima. Logarithmic barrier terms are assumed. For linear programming problems, such limits of both primal and dual trajectories - are strongly optimal, strictly complementary, and can be characterized as analytic centers of, loosely speaking, optimality regions. Examples are given, which show that those results do not hold in general for convex programming problems. If the latter are weakly analytic (Bank et al. [3]), primal trajectory limits can be characterized in analogy to the linear programming case and without assuming differentiability. That class of programming problems contains faithfully convex linear, and convex quadratic programming problems as strict subsets. In the differential case, dual trajectory limits can be characterized similarly, abeit under different conditions, one of which suffices for strict complementarity.
Citation
Mathematical Programming
Volume
90

Keywords

analytic center, barrier function, convex programming, degeneracy, interior point method, optimization, rank-integrity, SUMT, trajectory

Citation

McCormick, G. and Witzgall, C. (1999), Logarithmic SUMT Limits in Convex Programming, Mathematical Programming (Accessed May 22, 2024)

Issues

If you have any questions about this publication or are having problems accessing it, please contact reflib@nist.gov.

Created January 31, 1999, Updated October 12, 2021