【作者】 周伊佳；

【导师】 李博；

【作者基本信息】 青岛科技大学 ， 应用数学， 2011， 硕士

【摘要】 本文研究全局最优化问题,提出了全局优化问题的一些最优性条件,共分为四章。第一章介绍了全局最优化问题的历史以及研究现状,一些全局优化问题的基本定义和一般结论将在第二章中给出。第三章给出了一类新的全局最优解的条件:H -差商法。首先给出L-次梯度的概念,并据此给出H -差商和H -正规形的定义,再根据H -差商定义H -差商集,H -差商集是一些非线性函数所成的集合;然后得到关于特殊函数H -差商和H -正规形的全局最优解的充分必要条件。最后在第四章中,对于目标函数是非凸凹、非单调的非线性规划问题,给出了次正定函数的定义,并且给出了这类全局优化问题的一种新的凸凹化法。通过将目标函数直接凸化或凹化可以求得原问题的全局最优解。更多还原

【Abstract】 Several new optimality conditions for global optimization problem are proposed in this paper which contains four chapters. Global optimization problems’ history and the development are introduced in the first chapter. And then some fundamental definitions and conclusions are proposed in the second chapter. In the third chapter several new optimality conditions are studied : H-differential method. First H-differential and H-norma1 form are presented according to the L-subdifferential and then the H-differential set is also presented according to the H-differential. H-differential is a set of functions which are nonlinear functions. After that some necessary and sufficient conditions of global optimization have been obtained in terms of H-differential and H-norma1 form of special functions. In the last chapter a new method of convexification and concavification is also proposed by the definition of the subdefinite functions for the nonlinear programming problem in which the objective function is non-convex, non-concave, non-monotonous. With the objective function’s direct convexification or concavification, the global optimal solution can be easily reached.更多还原