用CDT和试验理论求解无约束最优化问题
On unconstrained optimization problems solved using CDT and triality theory
摘要：
DY Gao单独或与他的一些合作者应用他的规范对偶理论（CDT）解决了一类无约束最优化问题，得到了所谓的“triality定理”。不幸的是，2010年之前发表的这些结果中的“双极小对偶性”被证明是错误的，即使高岱年在2003年宣布获得它需要“某些附加条件”。2010年之后，高岱年和他的一些合作者发表了几篇论文，其中他们在triality定理中增加了获得“双极小”和“双极大”对偶性的附加条件。本文的目的是严格地处理这类问题，并讨论迄今为止有关“三重性理论”的几个结果。
英文摘要：
DY Gao solely or together with some of his collaborators applied his Canonical duality theory (CDT) for solving a class of unconstrained optimization problems, getting the so-called "triality theorems". Unfortunately, the "double-min duality" from these results published before 2010 revealed to be false, even if in 2003 DY Gao announced that "certain additional conditions" are needed for getting it. After 2010 DY Gao together with some of his collaborators published several papers in which they added additional conditions for getting "double-min" and "double-max" dualities in the triality theorems. The aim of this paper is to treat rigorously this kind of problems and to discuss several results concerning the "triality theory" obtained up to now.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
