From Semi-Infinite Programing problem to discuss the problem of separation of any two sets

• Main Authors: Ssu Yun Fang, 方思雲
• Other Authors: Soon Yi Wu
• Format: Others
• Language: en_US
• Published: 1999
• Online Access: http://ndltd.ncl.edu.tw/handle/32879733445591142927

碩士 === 國立成功大學 === 數學系 === 87 === It is an old mathematical problem that if there exits a hyperplane which will separate any two given sets. However, the LSIP proposed in the beginning of section 2 provides a constructive method. Besides, we also use the so-called "Cutting Plane Method" to discuss the solution procedure of the above LSIP and show that there will exist a subsequence of the solution sequence generated by "Cutting Plane Method" converging to the primal optimal solution. Finally, we find the dual problem of the primal LSIP and discuss under what condition will the optimal value of the primal equal to the optimal value of the dual.