A Branch and Contract Algorithm for Problems with Concave Univariate, Bilinear and Linear Fractional Terms

Authors:
Juan M. Zamora;Ignacio E. Grossmann
Affiliations:
Department of Chemical Engineering, Carnegie Mellon University Pittsburgh, PA 15213-3890, USA;Department of Chemical Engineering, Carnegie Mellon University Pittsburgh, PA 15213-3890, USA
Venue:
Journal of Global Optimization
Year:
1999

Citing 3
Cited 6

An analytical approach to global optimization

Mathematical Programming: Series A and B
Optimizing the sum of linear fractional functions

Recent advances in global optimization
Studies of the behavior of recursion for the pooling problem

ACM SIGMAP Bulletin

Semidefinite Relaxations of Fractional Programs via Novel Convexification Techniques

Journal of Global Optimization
On the Construction of Convex and Concave Envelope Formulas for Bilinear and Fractional Functions on Quadrilaterals

Computational Optimization and Applications
Improve-and-Branch Algorithm for the Global Optimization of Nonconvex NLP Problems

Journal of Global Optimization
A Lagrangean based branch-and-cut algorithm for global optimization of nonconvex mixed-integer nonlinear programs with decomposable structures

Journal of Global Optimization
Branching and bounds tighteningtechniques for non-convex MINLP

Optimization Methods & Software - GLOBAL OPTIMIZATION
A review of recent advances in global optimization

Journal of Global Optimization

Quantified Score

Hi-index	0.00

Visualization

Abstract

A new deterministic branch and bound algorithm is presented in this paper for the global optimization of continuous problems that involve concave univariate, bilinear and linear fractional terms. The proposed algorithm, the branch and contract algorithm, relies on the use of a bounds-contraction subproblem that aims at reducing the size of the search region by eliminating portions of the domain in which the objective function takes only values above a known upper bound. The solution of contraction subproblems at selected branch and bound nodes is performed within a finite contraction operation that helps reducing the total number of nodes in the branch and bound solution tree. The use of the proposed algorithm is illustrated with several numerical examples.