An Algorithm for Separable Piecewise Convex Programming Problems.
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)
Document Details
- Document Type
- Technical Report
- Publication Date
- Aug 01, 1971
- Accession Number
- AD0730755
Entities
People
- Richard M. Soland
Organizations
- University of Texas at Austin