Using the Dinkelbach-type algorithm to solve the continuous-time linear fractional programming problems

A Dinkelbach-type algorithm is proposed in this paper to solve a class of continuous-time linear fractional programming problems. We shall transform this original problem into a continuous-time non-fractional programming problem, which unfortunately happens to be a continuous-time nonlinear programm...

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Bibliographic Details
Published in:Journal of global optimization Vol. 49; no. 2; pp. 237 - 263
Main Authors: Wen, Ching-Feng, Wu, Hsien-Chung
Format: Journal Article
Language:English
Published: Boston Springer US 01.02.2011
Springer Nature B.V
Subjects:
Algorithms
Approximation
Computer Science
Linear programming
Mathematical functions
Mathematics
Mathematics and Statistics
Operations Research/Decision Theory
Optimization
Real Functions
Studies
Dinkelbach-type algorithm
Continuous-time linear fractional programming problems
Approximate solutions
Weak duality
Weak-star convergence
ISSN:0925-5001, 1573-2916
Online Access:Get full text
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Summary:A Dinkelbach-type algorithm is proposed in this paper to solve a class of continuous-time linear fractional programming problems. We shall transform this original problem into a continuous-time non-fractional programming problem, which unfortunately happens to be a continuous-time nonlinear programming problem. In order to tackle this nonlinear problem, we propose the auxiliary problem that will be formulated as parametric continuous-time linear programming problem. We also introduce a dual problem of this parametric continuous-time linear programming problem in which the weak duality theorem also holds true. We introduce the discrete approximation method to solve the primal and dual pair of parametric continuous-time linear programming problems by using the recurrence method. Finally, we provide two numerical examples to demonstrate the usefulness of this practical algorithm.
Bibliography:SourceType-Scholarly Journals-1
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ISSN:0925-5001
1573-2916
DOI:10.1007/s10898-010-9542-8