Convergence Analysis on Generic Algorithm for Solving Generalized Fractional Programming

• Main Authors: Hui-JuChen, 陳慧如
• Other Authors: Ruey-Lin Sheu
• Format: Others
• Language: en_US
• Published: 2010
• Online Access: http://ndltd.ncl.edu.tw/handle/84215337627572132580

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.