Accession Number : AD0730755

Title :   An Algorithm for Separable Piecewise Convex Programming Problems.

Descriptive Note : Research rept.,

Corporate Author : TEXAS UNIV AUSTIN CENTER FOR CYBERNETIC STUDIES

Personal Author(s) : Soland,Richard M.

Report Date : AUG 1971

Pagination or Media Count : 35

Abstract : The author presents a branch and bound algorithm to solve mathematical programming problems of the form: Find x = (x(1),...,x(n)) to minimize the summation of Phi(sub i 0)(x sub i) subject to x belongs to G, l < or = x < or = L, and the summation of Phi(sub i j) (x sub i) < or = O, j = 1,...,m. With l = (l(1,...,l(n)) and L = (L(1,...,L(n)), each Phi sub i j is is assumed to be lower semicontinuous and piecewise convex on the finite interval (l(i)L(i)). Gis assumed to be a closed convex set. The algorithm solves a finite sequence of convex programming problems; these correspond to successive partitions of the set C = the set(x/l< or = x < or = L) on the basis of the piecewise convexity of the problem functions (Phi sub i). Computational considerations are discussed, and an illustrative example is presented. (Author)

Descriptors :   (*MATHEMATICAL PROGRAMMING, CONVEX SETS), ALGORITHMS, SEQUENCES, MATHEMATICAL MODELS, MANAGEMENT ENGINEERING

Subject Categories : Operations Research

Distribution Statement : APPROVED FOR PUBLIC RELEASE