Continuous-Time Generalized Fractional Programming Problems. Part I: Basic Theory

This study, that will be presented as two parts, develops a computational approach to a class of continuous-time generalized fractional programming problems. The parametric method for finite-dimensional generalized fractional programming is extended to problems posed in function spaces. The develope...

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Bibliographic Details
Published in:Journal of optimization theory and applications Vol. 157; no. 2; pp. 365 - 399
Main Author: Wen, Ching-Feng
Format: Journal Article
Language:English
Published: Boston Springer US 01.05.2013
Springer Nature B.V
Subjects:
Applications of Mathematics
Approximation
Calculus of Variations and Optimal Control; Optimization
Computation
Discretization
Engineering
Euclidean space
Exact solutions
Function space
Linear programming
Mathematical analysis
Mathematics
Mathematics and Statistics
Operations Research/Decision Theory
Optimization
Programming
Theory of Computation
Infinite-dimensional nonlinear programming
Continuous-time generalized fractional programming problems
Strong duality
Parametric method
Continuous-time linear programming problems
ISSN:0022-3239, 1573-2878
Online Access:Get full text
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Summary:This study, that will be presented as two parts, develops a computational approach to a class of continuous-time generalized fractional programming problems. The parametric method for finite-dimensional generalized fractional programming is extended to problems posed in function spaces. The developed method is a hybrid of the parametric method and discretization approach. In this paper (Part I), some properties of continuous-time optimization problems in parametric form pertaining to continuous-time generalized fractional programming problems are derived. These properties make it possible to develop a computational procedure for continuous-time generalized fractional programming problems. However, it is notoriously difficult to find the exact solutions of continuous-time optimization problems. In the accompanying paper (Part II), a further computational procedure with approximation will be proposed. This procedure will yield bounds on errors introduced by the numerical approximation. In addition, both the size of discretization and the precision of an approximation approach depend on predefined parameters.
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ISSN:0022-3239
1573-2878
DOI:10.1007/s10957-012-0163-x