论文标题
一般变化不平等的新趋势
New Trends in General Variational Inequalities
论文作者
论文摘要
众所周知，一般的变异不平等为我们提供了一个统一，自然，新颖和简单的框架，以研究一系列无关的问题，这些问题是在纯净和应用的科学中出现的。在本文中，我们介绍了许多新的和已知的数值技术，用于使用各种技术解决一般的变异不平等和平衡问题，包括投影，Wiener-HOPF方程，动力学系统，辅助原理和惩罚函数。引入并研究了一般性变分的不平等现象。高阶的属性强烈概括了凸功能。辅助原理技术用于建议和分析一些解决高阶一般变异不平等的迭代方法。引入和讨论了一些新的一类强烈指数性的凸面功能。与其他方法相比，我们的收敛证明非常简单。我们的结果介绍了以前已知的解决变异不平等和相关优化问题的显着改善。由于一般的变分不平等包括（准）变异不平等和（准）隐式互补性问题作为特殊情况，因此这些结果继续存在这些问题。包括一些数值结果来说明所提出方法的效率。已经提出了一些开放问题，以在这些领域进行进一步研究。
It is well known that general variational inequalities provide us with a unified, natural, novel and simple framework to study a wide class of unrelated problems, which arise in pure and applied sciences. In this paper, we present a number of new and known numerical techniques for solving general variational inequalities and equilibrium problems using various techniques including projection, Wiener-Hopf equations, dynamical systems, auxiliary principle and penalty function. General variational-like inequalities are introduced and investigated. Properties of higher order strongly general convex functions have been discussed. The auxiliary principle technique is used to suggest and analyze some iterative methods for solving higher order general variational inequalities. Some new classes of strongly exponentially general convex functions are introduced and discussed. Our proofs of convergence are very simple as compared with other methods. Our results present a significant improvement of previously known methods for solving variational inequalities and related optimization problems. Since the general variational inequalities include (quasi) variational inequalities and (quasi) implicit complementarity problems as special cases, these results continue to hold for these problems. Some numerical results are included to illustrate the efficiency of the proposed methods. Several open problems have been suggested for further research in these areas.
