Continuous Min-Max Problems and Fractional Programs--An Entropic Approach and Extensions

• Main Authors: Jen-Yen Lin, 林仁彥
• Other Authors: Ruey-Lin Sheu
• Format: Others
• Language: en_US
• Published: 2006
• Online Access: http://ndltd.ncl.edu.tw/handle/93001741107708831630

博士 === 國立成功大學 === 數學系應用數學碩博士班 === 94 === 　In this dissertation, we study algorithms for solving continuous min-max problem with an extension to fractional programs. We propose an iterative entropic regularization method that reduces the continuous min-max problem into a sequence of finite min-max problems and also allows estimation for the error bounds. The method is then combined with the Dinkelbach-type algorithm to solve the continuous min-max fractional program. Finally, the Dinkelbach-type algorithm is extended to solve more general fractional programs including the difficult sum-of-ratio problem. All algorithms are equipped with convergence analysis as well as numerical examples to show the correctness and the robustness.