Branch-and-Bound Outer Approximation Algorithm for Sum-of-Ratios Fractional Programs

In this article, a branch and-bound outer approximation algorithm is presented for globally solving a sum-of-ratios fractional programming problem. To solve this problem, the algorithm instead solves an equivalent problem that involves minimizing an indefinite quadratic function over a nonempty, com...

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Bibliographic Details
Published in:Journal of optimization theory and applications Vol. 146; no. 1; pp. 1 - 18
Main Author: Benson, H. P.
Format: Journal Article
Language:English
Published: Boston Springer US 01.07.2010
Springer
Springer Nature B.V
Subjects:
Algorithms
Applications of Mathematics
Applied sciences
Approximation
Bond portfolios
Branch & bound algorithms
Calculus of Variations and Optimal Control; Optimization
Computation
Engineering
Equivalence
Exact sciences and technology
Mathematical analysis
Mathematical models
Mathematical programming
Mathematics
Mathematics and Statistics
Operational research and scientific management
Operational research. Management science
Operations management
Operations Research/Decision Theory
Optimization
Programming
Ratios
Studies
Theory of Computation
Global optimization
Fractional programming
Outer approximation
Branch and bound
Sum of ratios
Convex set
Compact space
Linear form
Branch and bound method
Minimization
Global optimum
Approximation algorithm
Modeling
Convex programming
Exact solution
Rational function
Quadratic function
Mathematical programming
ISSN:0022-3239, 1573-2878
Online Access:Get full text
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Description
Summary:In this article, a branch and-bound outer approximation algorithm is presented for globally solving a sum-of-ratios fractional programming problem. To solve this problem, the algorithm instead solves an equivalent problem that involves minimizing an indefinite quadratic function over a nonempty, compact convex set. This problem is globally solved by a branch-and-bound outer approximation approach that can create several closed-form linear inequality cuts per iteration. In contrast to pure outer approximation techniques, the algorithm does not require computing the new vertices that are created as these cuts are added. Computationally, the main work of the algorithm involves solving a sequence of convex programming problems whose feasible regions are identical to one another except for certain linear constraints. As a result, to solve these problems, an optimal solution to one problem can potentially be used to good effect as a starting solution for the next problem.
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ISSN:0022-3239
1573-2878
DOI:10.1007/s10957-010-9647-8