Concave programming and piece- wise linear programming

Research output: Contribution to journalArticle

8 Citations (Scopus)

Abstract

This paper discusses the mathematical foundations of a technique that has been used extensively in structural optimization. Two basic problems are considered. The first of these is the concave programming problem which consists of finding the global minimum of piece wise concave functions' on 'piece- wise concave sets'. Since any function can be approximated by a piece- wise concave function, this method could in principle be used to find the global minimum in nonconvex optimization problems. The second one is the piece- wise linear programming problem in which the objective function is convex and piece- wise linear. The iterative method outlined for handling this problem is shown to be much more efficient than the standard simplex method of linear programming.

Original languageEnglish
Pages (from-to)131-144
Number of pages14
JournalInternational Journal for Numerical Methods in Engineering
Volume3
Issue number1
Publication statusPublished - Jan 1971

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Piecewise Linear
Linear programming
Programming
Concave function
Global Minimum
Nonconvex Optimization
Simplex Method
Nonconvex Problems
Structural optimization
Structural Optimization
Iterative methods
Objective function
Optimization Problem
Iteration

ASJC Scopus subject areas

  • Engineering (miscellaneous)
  • Computational Mechanics
  • Applied Mathematics

Cite this

Concave programming and piece- wise linear programming. / Rozvany, G.

In: International Journal for Numerical Methods in Engineering, Vol. 3, No. 1, 01.1971, p. 131-144.

Research output: Contribution to journalArticle

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