Piecewise-Linear Pathways to the Optimal Solution Set in Linear Programming

M. Ç. Pinar
Additional contact information
M. Ç. Pinar: Bilkent University

Journal of Optimization Theory and Applications, 1997, vol. 93, issue 3, No 11, 619-634

Abstract: Abstract This paper takes a fresh look at the application of quadratic penalty functions to linear programming. Recently, Madsen et al. (Ref. 1) described a continuation algorithm for linear programming based on smoothing a dual l 1-formulation of a linear program with unit bounds. The present paper is prompted by the observation that this is equivalent to applying a quadratic penalty function to the dual of a linear program in standard canonical form, in the sense that both approaches generate continuous, piecewise-linear paths leading to the optimal solution set. These paths lead to new characterizations of optimal solutions in linear programming. An important product of this analysis is a finite penalty algorithm for linear programming closely related to the least-norm algorithm of Mangasarian (Ref. 2) and to the continuation algorithm of Madsen et al. (Ref. 1). The algorithm is implemented, and promising numerical results are given.

Keywords: Quadratic penalty functions; linear programming; piece-wise-linear path-following algorithms; characterization of optimal solutions; finiteness (search for similar items in EconPapers)
Date: 1997
References: View complete reference list from CitEc
Citations: View citations in EconPapers (1)

Downloads: (external link)
http://link.springer.com/10.1023/A:1022651331550 Abstract (text/html)
Access to the full text of the articles in this series is restricted.

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:spr:joptap:v:93:y:1997:i:3:d:10.1023_a:1022651331550

Ordering information: This journal article can be ordered from
http://www.springer. ... cs/journal/10957/PS2

DOI: 10.1023/A:1022651331550

Access Statistics for this article

Journal of Optimization Theory and Applications is currently edited by Franco Giannessi and David G. Hull

More articles in Journal of Optimization Theory and Applications from Springer
Bibliographic data for series maintained by Sonal Shukla () and Springer Nature Abstracting and Indexing ().