Taiwanese Journal of Mathematics

AN INTERVAL-TYPE ALGORITHM FOR CONTINUOUS-TIME LINEAR FRACTIONAL PROGRAMMING PROBLEMS

Ching-Feng Wen

Full-text: Open access

Abstract

An interval-type computational procedure by combining the parametric method and discretization approach is proposed in this paper to solve a class of continuous-time linear fractional programming problems (CLFP). Using the different step sizes of discretization problems, we construct a sequence of convex, piecewise linear and strictly decreasing upper and lower bound functions. The zeros of upper and lower bound functions then determine a sequence of intervals shrinking to the optimal value of (CLFP) as the size of discretization getting larger. By using the intervals we can find corresponding approximate solutions to (CLFP). We also establish upper bounds of lengths of these intervals, and thereby we can determine the size of discretization in advance such that the accuracy of the corresponding approximate solution can be controlled within the predefined error tolerance. Moreover, we prove that the searched sequence of approximate solution functions weakly-star converges to an optimal solution of (CLFP). Finally, we provide some numerical examples to implement our proposed method.

Article information

Source
Taiwanese J. Math., Volume 16, Number 4 (2012), 1423-1452.

Dates
First available in Project Euclid: 18 July 2017

Permanent link to this document
https://projecteuclid.org/euclid.twjm/1500406742

Digital Object Identifier
doi:10.11650/twjm/1500406742

Mathematical Reviews number (MathSciNet)
MR2951146

Zentralblatt MATH identifier
1286.90147

Subjects
Primary: 90C32: Fractional programming 90C48: Programming in abstract spaces

Keywords
continuous-time linear programming problems continuous-time linear fractional programming problems infinite-dimensional linear programming problems interval-type algorithm

Citation

Wen, Ching-Feng. AN INTERVAL-TYPE ALGORITHM FOR CONTINUOUS-TIME LINEAR FRACTIONAL PROGRAMMING PROBLEMS. Taiwanese J. Math. 16 (2012), no. 4, 1423--1452. doi:10.11650/twjm/1500406742. https://projecteuclid.org/euclid.twjm/1500406742


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