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

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

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Article ID: iaor20132834
Volume: 157
Issue: 2
Start Page Number: 365
End Page Number: 399
Publication Date: May 2013
Journal: Journal of Optimization Theory and Applications
Authors:
Keywords: programming: fractional
Abstract:

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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