Regional Gradient-Constrained Control Problem. Approaches and Simulations

In this paper, we study an optimal control problem with gradient constraints for linear parabolic systems. Our analysis is based on subdifferential techniques and on Lagrangian multiplier method to characterize the optimal control. We also give numerical scheme for the computation of such a control. The simulations illustrate successfully the obtained results and lead to some conjectures.     

One more Global Property of ε-Subdifferentials

The paper presents one more global interrelation between the values of a convex function and its -subdifferential. A direct consequence of this interrelation is the proof of the fact that functions with identical -subdifferentials have an identical limit behavior.     

Stability and Duality of Nonconvex Problems via Augmented Lagrangian

A nonconvex mathematical programming problem on a topological linear space in the presence of an inequality constraint is considered. An augmented Lagrangian function is constructed by using supporting cones to the epigraph of a usual perturbation function. Extremal values of prime and dual problems are shown to be equivalent under the stability conditions derived.     

E次微分的一些新性质

相应于凸规划的凸集和凸函数自寺性质已有很多结论,并且在凸规划的研究中得到了充分应用。相应于广义凸规划-E凸规划的E凸集和E凸函数的性质目前的研究结果还不多。在凸集、凸函数的已有结论以及E凸集和E凸函数的现有研究结果的基础上,结合Rockafeller的基本思想对E凸函数的次微分进行了探讨,给出了次微分的共轭性,连续性,以及单调性等一些结论。这些结果对广义凸规划-E凸规划的研究可能会起到一定的促进作用。关于E凸集、E凸函数和E凸规划的性质还需要人们进行深入彻底的研究。     

锥凸集值映射的锥次微分的存在性

在局部凸线性拓扑向量空间讨论了一种锥凸集值映射的锥次微分的存在 性问题,证明了几个锥次微分的存在定理。     

The Ki-Fan Inequality and Operator Inclusions in Banach Spaces

The paper presents the generalized Ki-Fan inequality and its application to the solvability of operator inclusions in reflexive Banach spaces.     

鲁棒多目标优化问题ε - 拟弱有效解的最优性条件

研究了约束函数带有不确定因素的多目标鲁棒优化问题的最优性条件.首先,利用变分分析的工具(最大值函数的次微分、中值不等式、极限次微分的和规则等)建立不确定多目标优化问题的鲁棒ε- 拟弱有效解的最优性必要条件; 然后,在伪拟广义凸性的假设下,给出了该问题的最优性充分条件; 最后,用实例证明了相关结论的正确性.