Finiteness in restricted simplicial decomposition

D. W. Hearn, S. Lawphongpanich, Jose Antonio Ventura

Research output: Contribution to journalArticle

42 Scopus citations


Simplicial decomposition is an important form of decomposition for large non-linear programming problems with linear constraints. Von Hohenbalken has shown that if the number of retained extreme points is n + 1, where n is the number of variables in the problem, the method will reach an optimal simplex after a finite number of master problems have been solved (i.e., after a finite number of major cycles). However, on many practical problems it is infeasible to allocate computer memory for n + 1 extreme points. In this paper, we present a version of simplicial decomposition where the number of retained extreme points is restricted to r, 1 ≤ r ≤ n + 1, and prove that if r is sufficiently large, an optimal simplex will be reached in a finite number of major cycles. This result insures rapid convergence when r is properly chosen and the decomposition is implemented using a second order method to solve the master problem.

Original languageEnglish (US)
Pages (from-to)125-130
Number of pages6
JournalOperations Research Letters
Issue number3
StatePublished - Jan 1 1985

All Science Journal Classification (ASJC) codes

  • Management Science and Operations Research
  • Statistics, Probability and Uncertainty
  • Discrete Mathematics and Combinatorics
  • Modeling and Simulation

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