Convergence Analysis on Generic Algorithm for Solving Generalized Fractional Programming
博士 === 國立成功大學 === 數學系應用數學碩博士班 === 98 === In this dissertation, we propose a generic algorithm for solving generalized fractional programming. Classical Dinkelbach-type algorithms such as the original Dinkelbach-type algorithm, the ``dual" algorithm and the interval-type algorithm selected speci...
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| Format: | Others |
| Language: | en_US |
| Published: |
2010
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| Online Access: | http://ndltd.ncl.edu.tw/handle/84215337627572132580 |
| Summary: | 博士 === 國立成功大學 === 數學系應用數學碩博士班 === 98 === In this dissertation, we propose a generic algorithm for solving generalized fractional programming. Classical Dinkelbach-type algorithms such as the original Dinkelbach-type algorithm, the ``dual" algorithm and the interval-type algorithm selected specific iterate parameters and proved the convergence with complicate analysis. Our generic algorithm is a natural and simple refinement of the interval-type algorithm. It not only unifies existing
versions of classical Dinkelbach-type algorithms, but gives a stronger convergence result and convergence rate analysis by way of geometric observations and fundamental properties of convex functions. As a result, the classical results are strengthened with new insights.
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