AN ALGORITHM FOR SEPARABLE NONCONVEX PROGRAMMING PROBLEMS.

Abstract

An algorithm is presented for solving mathematical programming problems of the form: Find chi = (chi sub one, ..., chi sub n) to minimize Summation (Phi sub i (chi sub i)) subject to chi) an element of G and l = or < chi = or < L. Each Phi sub i is assumed to be lower semicontinuous, possibly nonconvex, and G is assumed to be closed. The algorithm is of the branch-and-bound type and solves a sequence of problems in each of which the objective function is convex. These problems correspond to successive partitions of the feasible set. Two different rules for refining the partitions are considered; these lead to convergence of the algorithm under different requirements on the problem functions. Examples are given and computational considerations are discussed. (Author)

Document Details

Document Type
Technical Report
Publication Date
Jul 01, 1968
Accession Number
AD0672084

Entities

People

  • James E. Falk
  • Richard M. Soland

Tags

DTIC Thesaurus Topics

  • Algorithms
  • Computer Programming
  • Convergence
  • Evolutionary Algorithms
  • Heuristic Methods
  • Mathematical Programming
  • Mathematics
  • Nonconvex Programming
  • Refining
  • Sequences

Readers

  • Calculus or Mathematical Analysis
  • Operations Research