Non-Linear Programming Via Penalty Functions
The non-linear programming problem seeks to maximize a function f(x) where the n component vector x must satisfy certain constraints g i(x) - 0, i - 1, ..., m 1 and g i(z) \geqq 0, i - m 1 + 1, ..., m. The algorithm presented in this paper solves the non-linear programming problem by transforming it into a sequence of unconstrained maximization problems. Essentially, a penalty is imposed whenever x does not satisfy the constraints. Although the algorithm appears most useful in the concave case, the convergence proof holds for non-concave functions as well. The algorithm is especially interesting in the concave case because the programming problem reduces to a single unconstrained maximization problem or, at most, to a finite sequence of unconstrained maximization problems. In addition, the paper presents a new class of dual problems, and the algorithm is shown to be a dual feasible method. Another property of the algorithm is that it appears particularly well suited for large-scale problems with a sizable number of constraints.
Volume (Year): 13 (1967)
Issue (Month): 5 (January)
|Contact details of provider:|| Postal: |
Web page: http://www.informs.org/
More information through EDIRC
When requesting a correction, please mention this item's handle: RePEc:inm:ormnsc:v:13:y:1967:i:5:p:344-358. 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 references are entirely missing, you can add them using this form.