Algorithms for Special Nonlinear Programming Problems

本项目主要研究非光滑罚函数在非线性规划方法中的应用，特别是在半无限规划、复线性逼近、Nor-L-One和约束最优控制等领域。罚函数通常具有复杂的结构，或者是非光滑的，这使得有必要设计特殊的技巧来最小化它们。这位研究人员计划将已知的算法扩展和应用到非线性规划的一些新领域。从这个角度出发，我们将研究四个方面：复杂的L-One逼近、二阶修正方法的不精确性、半无限规划和离散化的最优控制问题。将解决算法问题，并将在超级计算机上进行数值实验。这项研究属于非线性规划和计算优化的一般领域，在工程和管理科学中有许多应用。

This project focuses on the use of nonsmooth penalty functions in nonlinear programming methods, in particular in the areas of semi-infinite programming, complex linear approximation in the nor l-one and constrained optimal control. Penalty functions usually have complicated structure, or else are nonsmooth, making it necessary to devise special techniques for their minimization. The investigator plans to extend and apply known algorithms to some new areas of nonlinear programming. Four areas will be investigated from this point of view: complex l-one approximations, inexactness of the second-order correction method, semi-infinite programming and discretized optimal control problems. Algorithmic questions will be addressed, and numerical experiments will be performed on a supercomputer. This research falls into the general area of nonlinear programming and computational optimization which has numerous applications in engineering and management science.