In this paper, we consider approximate solutions (also called $\varepsilon$-solutions) for semi-infinite optimization problems that objective function and constraint functions with uncertainty data are all convex, and establish robust counterpart of convex semi-infinite program and then consider approximate solutions for its. Moreover, the robust necessary condition and robust sufficient theorems are obtained. Then the duality results of the Lagrangian dual approximate solution is given by the robust optimization approach under a cone constraint qualification.

In this paper, we mainly study the dual problem of the nonconvex semi-infinite programming problem with inequality constraints. It is well known that there is usually a duality gap in constructing duality problem using the ordinary Lagrangian function. To eliminate the duality gap, we construct an augmented Lagrangian function, then discuss its duality. Under reasonable assumptions, the strong duality theorem between the primal problem and the augmented Lagrangian dual problem holds. Finally, an example is given to verify the presented results.

In this paper,we propose a nonmonotone trust region filter method for minimax problems.In the presented algorithm,based on the filter technique,the acceptable criterion of the trial points is relaxed,so compared to the existing Seqential quadratic programming(SQP)Newton-type methods for minimax problems,our method is more flexible.Under some suitable conditions,the global convergence properties are established.The numerical tests are reported in the end.

求解极大极小问题的灵活非单调滤子方法与传统的滤子方法相比,对于试探步的可接受性,该方法具有更大的灵活性,而且与单调型方法相比,计算量更小.此外,还利用一个自适应参数来调整接受准则,从而在一定程度上避免了Maratos效应.在合理的假设下,该算法具有全局收敛性,并且通过数值实验验证了该方法的有效性.

在"互联网+"新常态背景下,无论是高校教师还是高校管理者、大学生群体在高校党建工作中都要做到多创新,注重党建工作责任制内容的有效优化,从基层落实创新理念,为高校党建工作注入活力,迎接美好未来.本文对"互联网+"模式下高校党建工作创新研究进行了探讨.

本文提出一个解决不等式规划问题的无罚无滤子的修正非单调不可行QP-free算法.在每步迭代,只需要解两个或三个相同系数矩阵来获得搜索方向.我们利用修正的非单调技术松弛了试探点的判别准则,相比其他方法,不要求滤子结构也不涉及罚参数的选取,在一定程度上避免了Maratos效应.在合理的条件下,得到算法的全局收敛性.

The current sequential quadratic programming (SQP) type algorithm may fail if the QP subproblem is infeasible.Moreover the choice of penalty function in line search is difficult.In [1],the author modified the SQP method for the former problem.In this paper,on the base of paper [1],a line search filter search technique is presented to conquer the second problem.Under some conditions,the global convergence of the algorithm in this paper has shown at the end.