【作者】 李凤莲；

【导师】 丁协平；

【作者基本信息】 四川师范大学 ， 基础数学， 2007， 硕士

【摘要】 与其它类型算法相比，变分不等式的投影算法构造简洁。因此该算法被研究变分不等式算法的学者深入而细致地讨论。但早期投影算法的收敛性证明通常要求变分不等式中的映射是强单调和Lipschitz连续的。二次投影算法是近年来针对经典变分不等式提出的一类新的投影算法，它最大的优点是算法的收敛性证明只要求映射是伪单调和连续的。广义变分不等式不仅包含经典变分不等式作为特例，而且有更广泛的应用背景。迄今为止，针对广义变分不等式提出的算法通常假设映射是强单调和Lipschitz连续的。本文探讨将二次投影算法推广到广义变分不等式问题，算法及其收敛性证明仅要求映射是伪单调和连续的。其次，本文讨论了一类随机变分不等式的迭代算法。最后，局部凸空间中的一个Farkas引理被证明，它不仅推广了已知的结果，而且证明方法更简洁。更多还原

【Abstract】 Compared to other algorithms for variational inequalities, pro-jection methods are conceptually simple methods. It is because of this reasonthat projection methods have been intensively studied in the literature. Earlyalgorithms of projection type usually assume the map involved is stronglymonotone and/or Lipschitz continuous. Double projection algorithm im-proves those earlier projection algorithms by assuming the map to be onlypseudomonotone and continuous. Though early projection algorithms havealready been extended to generalized variation inequalities, the double pro-jection algorithm has not been done so. This paper concentrates on studyingdouble projection algorithm for generalized variational inequalities. More-over, a projection algorithm for a class of stochastic variational inequalitiesis discussed, and a Farkas lemma is proved in locally convex spaces whichnot only generalizes known result to more general spaces but also is provedin a simpler way.更多还原