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

Authors:
Ching-Feng Wen;Hsien-Chung Wu
Affiliations:
Center for General Education, Kaohsiung Medical University, Kaohsiung, Taiwan 807;Department of Mathematics, National Kaohsiung Normal University, Kaohsiung, Taiwan 802
Venue:
Journal of Global Optimization
Year:
2011

Citing 9
Cited 0

An algorithm for a class of continuous linear programs

SIAM Journal on Control and Optimization
On the Solutions of a Class of Continuous Linear Programs

SIAM Journal on Control and Optimization
Forms of Optimal Solutions for Separated Continuous Linear Programs

SIAM Journal on Control and Optimization
A Duality Theory for Separated Continuous Linear Programs

SIAM Journal on Control and Optimization
Optimality conditions and duality for a class of nonlinear fractional programming proglems

Journal of Optimization Theory and Applications
Convergence of a General Class of Algorithms for Separated Continuous Linear Programs

SIAM Journal on Optimization
Efficient Algorithms for Separated Continuous Linear Programs: The Multicommodity Flow Problem with Holding Costs and Extensions

Mathematics of Operations Research
A simplex based algorithm to solve separated continuous linear programs

Mathematical Programming: Series A and B
A recurrence method for a special class of continuous time linear programming problems

Journal of Global Optimization

Quantified Score

Hi-index	0.00

Visualization

Abstract

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.