An Improved Successive Linear Programming Algorithm

Jianzhong Zhang, Nae-Heon Kim and L. Lasdon
Additional contact information
Jianzhong Zhang: Department of Mathematics, Shanghai Normal University, Shanghai, Peoples Republic of China
Nae-Heon Kim: Department of Mechanical Engineering, Ajoy University, San 5 Wonchudon, Suwon, Korea
L. Lasdon: Department of General Business and IC 2 Institute, University of Texas, Austin, Texas 78712

Management Science, 1985, vol. 31, issue 10, 1312-1331

Abstract: Successive Linear Programming (SLP) algorithms solve nonlinear optimization problems via a sequence of linear programs. They have been widely used, particularly in the oil and chemical industries, beginning with their introduction by Griffith and Stewart of Shell Development Company in 1961. Since then, several applications and variants of SLP have appeared, the most recent being the SLPR algorithm described in this journal in 1982 (Palacios-Gomez et al.). SLP procedures are attractive because they are fairly easy to implement if an efficient, flexible LP code is available, can solve nonseparable as well as separable problems, can be applied to as large a problem as the LP code can handle (often thousands of constraints and variables), and have been successful in many practical applications. This paper describes a new SLP algorithm called PSLP (Penalty SLP). PSLP represents a significant strengthening and refinement of the SLPR procedure described in Palacios-Gomez et al. (Palacios-Gomez, F., L. Lasdon, M. Engquist. 1982. Nonlinear optimization by successive linear programming. Management Sci. 28 1106--1120.). We give a convergence proof for PSLP---the first SLP convergence proof for nonlinearly constrained problems of general form. This theory is supported by computational performance---in our tests, PSLP is significantly more robust than SLPR, and at least as efficient. A Fortran computer implementation is described. A simplified version of PSLP has already solved several "real world" NLP problems at Exxon (Baker and Lasdon [Baker, T. E., L. S. Lasdon. 1985. Successive linear programming at Exxon. Management Sci. 31 (March) 264--274.), including nonlinear refinery models of up to 1000 rows. As with other SLP algorithms, PSLP is especially efficient on problems which are highly constrained, i.e., which have nearly as many active constraints as there are variables. For problems with vertex optima (at least as many active constraints as variables), it is quadratically convergent. Nonlinear refinery models often have vertex optima, since they are large and mostly linear, and on line process unit optimization problems are likely to possess highly constrained solutions as well. PSLP has great potential for accurate, efficient solution of such problems.

Keywords: nonlinear; programming (search for similar items in EconPapers)
Date: 1985
References: Add references at CitEc
Citations: View citations in EconPapers (15)

Downloads: (external link)
http://dx.doi.org/10.1287/mnsc.31.10.1312 (application/pdf)

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:inm:ormnsc:v:31:y:1985:i:10:p:1312-1331

Access Statistics for this article

More articles in Management Science from INFORMS Contact information at EDIRC.
Bibliographic data for series maintained by Chris Asher ().