Continuous-Time Generalized Fractional Programming Problems, Part II: An Interval-Type Computational Procedure

The theory presented in Part I (Wen in J. Optim. Theory Appl. 2012) of this study led to a theoretical parametric procedure for continuous-time generalized fractional programming problems. In this paper (Part II), an interval-type computational procedure by combining the parametric method and discre...

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Vydáno v:Journal of optimization theory and applications Ročník 156; číslo 3; s. 819 - 843
Hlavní autor: Wen, Ching-Feng
Médium: Journal Article
Jazyk:angličtina
Vydáno: Boston Springer US 01.03.2013
Springer Nature B.V
Témata:
Accuracy
Algorithms
Applications of Mathematics
Approximation
Calculus of Variations and Optimal Control; Optimization
Computation
Computational mathematics
Discretization
Engineering
Errors
Euclidean space
Linear programming
Mathematical models
Mathematics
Mathematics and Statistics
Nonlinear programming
Operations Research/Decision Theory
Optimization
Optimization algorithms
Programming
Simplification
Studies
Theory
Theory of Computation
Tolerances
Infinite-dimensional nonlinear programming
Continuous-time generalized fractional programming problems
Strong duality
Interval-type algorithm
Continuous-time linear programming problems
ISSN:0022-3239, 1573-2878
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Shrnutí:The theory presented in Part I (Wen in J. Optim. Theory Appl. 2012) of this study led to a theoretical parametric procedure for continuous-time generalized fractional programming problems. In this paper (Part II), an interval-type computational procedure by combining the parametric method and discretization approach is proposed. The proposed method is promising particularly when it is acceptable to find an effective, but near-optimal value in an efficient manner. Once the error tolerance is predetermined, 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. Hence, the trade-off between the quality of the results and the simplification of the problem can be controlled by the decision maker. Finally, we provide some numerical examples to implement our proposed method.
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ISSN:0022-3239
1573-2878
DOI:10.1007/s10957-012-0131-5