非线性二阶微分不等式组的Optimization
Optimization of System of Nonlinear Second Order Differential Inequalities
摘要：
本文讨论了具有凸与非凸、离散与可微的二阶状态变量不等式约束的Bolza问题的最优化问题，给出了最优性的充要条件。根据所提出的离散化方法和次微分包含的等价定理，研究了离散逼近不等式组问题，该问题对导出由给定的非线性不等式约束产生的伴随离散包含有重要意义.在极限情形下，得到了连续问题最优性的充分条件。最后给出了一个数值例子来说明理论结果。
英文摘要：
This paper deals with the optimization of Bolza problem with a system of convex and nonconvex, discrete and differential state variable inequality constraints of second order by deriving necessary and sufficient conditions for optimality. According to proposed discretization method and equivalence theorems for subdifferential inclusions, the problem with a system of discrete-approximation inequalities are investigated which highly contributes to the derivation of adjoint discrete inclusions generated by given system of nonlinear inequality constraints. Moreover, in the limit case, we obtain sufficient conditions for optimality of the continuous problem. A numerical example is presented to illustrate the theoretical result.
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