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

Tags

DTIC Thesaurus Topics

  • Algorithms
  • Computer Programming
  • Convex Programming
  • Convex Sets
  • Evolutionary Algorithms
  • Heuristic Methods
  • Intervals
  • Mathematical Programming
  • Mathematics
  • Sequences

Fields of Study

  • Mathematics

Readers

  • Calculus or Mathematical Analysis
  • Finite Element Method (FEM) for solving Partial Differential Equations (PDEs)
  • Mathematical Modeling and Probability Theory.