【作者】 张海森；

【导师】 何诣然；

【作者基本信息】 四川师范大学 ， 应用数学， 2010， 硕士

【摘要】 本文将广义拟变分不等式和非光滑拟变分不等式问题转化为关于正则化间隙函数的极小化问题.在最优化问题中,研究目标函数的方向导数及其次微分具有重要意义,如利用目标函数的方向导数和次微分讨论最优性条件,建立基于方向导数或次微分的优化算法.本文讨论了边际函数的方向可微性和一类含参变量凸规划问题的边际函数的Clarke方向导数的上界和下界.利用这些结果,我们研究了广义拟变分不等式问题的正则化间隙函数的方向可微性及极限次微的上界和非光滑拟变分不等式的正则化间隙函数和D-间隙函数的Clarke方向导数.更多还原

【Abstract】 In this paper, we use regularized gap functions to reformulate quasi-variational inequalities into minimization problems. In optimization prob-lems, it is significant to study the directional derivatives and subdifferentials of objective function, for example, we can use the directional derivatives and sub-differentials of objective function to study the necessary optimality conditions and algorithms for optimization problems. We discuss the directional differentia-bility of marginal function and estimate the upper and lower bounds of a class of marginal functions in parametric convex programs. Then we employ these results to study the directional differentiability and the upper bound of limit-subdifferentials of the regularized gap functions for generalized quasi-variational inequalities and Clarke directional derivatives of the regularized gap functions and D-gap functions for nonsmooth quasi-variational inequalities.更多还原