An Improved Successive Linear Programming Algorithm
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.
Volume (Year): 31 (1985)
Issue (Month): 10 (October)
|Contact details of provider:|| Postal: 7240 Parkway Drive, Suite 300, Hanover, MD 21076 USA|
Web page: http://www.informs.org/
More information through EDIRC
When requesting a correction, please mention this item's handle: RePEc:inm:ormnsc:v:31:y:1985:i:10:p:1312-1331. See general information about how to correct material in RePEc.
For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: (Mirko Janc)
If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.
If references are entirely missing, you can add them using this form.
If the full references list an item that is present in RePEc, but the system did not link to it, you can help with this form.
If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your profile, as there may be some citations waiting for confirmation.
Please note that corrections may take a couple of weeks to filter through the various RePEc services.