### 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 language | English |
---|---|

Pages (from-to) | 131-144 |

Number of pages | 14 |

Journal | International Journal for Numerical Methods in Engineering |

Volume | 3 |

Issue number | 1 |

Publication status | Published - Jan 1971 |

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### ASJC Scopus subject areas

- Engineering (miscellaneous)
- Computational Mechanics
- Applied Mathematics

### Cite this

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

Research output: Contribution to journal › Article

*International Journal for Numerical Methods in Engineering*, vol. 3, no. 1, pp. 131-144.

}

TY - JOUR

T1 - Concave programming and piece- wise linear programming

AU - Rozvany, G.

PY - 1971/1

Y1 - 1971/1

N2 - 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.

AB - 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.

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UR - http://www.scopus.com/inward/citedby.url?scp=0014997312&partnerID=8YFLogxK

M3 - Article

AN - SCOPUS:0014997312

VL - 3

SP - 131

EP - 144

JO - International Journal for Numerical Methods in Engineering

JF - International Journal for Numerical Methods in Engineering

SN - 0029-5981

IS - 1

ER -