解一类似变分不等式问题的预解式技术与辅助原理技术

Resolvent Operator Technique and Auxiliary Principle for Solving a Class of Variational-like Inequaties

在研究变分不等式问题 ,特别是解的逼近时 ,通常要借助于真凸下半连续泛函的次微分算子的预解算子 ,运用Banach不动点定理逼近变分不等式问题的解 .而针对似变分不等式问题 ,方法之一是构造一系列辅助问题来逼近问题的解———即辅助原理技术 .另一种新颖的方法是借助于 η 次微分的概念 ,构造 η 次微分算子的预解式来逼近问题的解 .运用 η 次微分算子的预解式技术和辅助原理技术给出了一类似变分不等式问题解的存在性和唯一性 .

When we study variational inequalities, in particular approximating to the solution, we often resort to resolvent operator of subdifferential operator of proper convex lower semi continuous function, using Banach's theorems on fired points, to approximate to the solution of variational inequalities. As for variational like inequalities, one method called auxiliary principle is to construct a series of auxiliary problems to approximate to the original solution. Another new method is to construct resolvent operator by using the concept of η subdifferential, resolvent operator technique and auxiliary principle technique, we present the existence and uniqueness of the solution of a class of variational like inequalities.