变分不等式的应用

The Application of The Variational Inequality

本文涉及了变分不等式以及各项应用,给出了其一些性质的讨论,还有用变分法解决一些最小值问题的思想,比如火箭最优控制问题。

The variational inequality originates in physical and mathematic problems. In the mid-- 1960s, there exists the complementarity of the linear and nonlinear problems in researching the nonlinear programming. They have further developed to the variational inequality in the finite--dimensional space. and nonlinear programming problems. In the 1970s, the variational inequality is widely used in the optimal control problems, the elasticity problems, the elastoplastic problems and the Seepage problems. This arti- cle deals with variational inequalities and the application of variational inequalities, and discusses its prop- erties. Moreover, it uses some variational method to solve the minimum problems, for example, the appli- cations to the optimal control of rockets.