ISSN:
1436-4646
Keywords:
Disjunctive programming
;
reverse convex programming
;
facial disjunctive sets
;
convex hull generation
Source:
Springer Online Journal Archives 1860-2000
Topics:
Computer Science
,
Mathematics
Notes:
Abstract This paper is about a property of certain combinatorial structures, called sequential convexifiability, shown by Balas (1974, 1979) to hold for facial disjunctive programs. Sequential convexifiability means that the convex hull of a nonconvex set defined by a collection of constraints can be generated by imposing the constraints one by one, sequentially, and generating each time the convex hull of the resulting set. Here we extend the class of problems considered to disjunctive programs with infinitely many terms, also known as reverse convex programs, and give necessary and sufficient conditions for the solution sets of such problems to be sequentially convexifiable. We point out important classes of problems in addition to facial disjunctive programs (for instance, reverse convex programs with equations only) for which the conditions are always satisfied. Finally, we give examples of disjunctive programs for which the conditions are violated, and so the procedure breaks down.
Type of Medium:
Electronic Resource
URL:
http://dx.doi.org/10.1007/BF01587096
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