完整代码，可直接运行

Given symmetric matrices B,D ∈ R n×n and a symmetric positive definite matrix W ∈ R n×n , maximizingthe sum of the Rayleighquotientx ? Dx andthe gener- alized Rayleigh quotient x ? Bx x ? Wx on the unit sphere not only is of mathematical interest in its own right, but also finds applications in practice. In this paper, we first present a real world application arising from the sparse Fisher discriminant analysis. To tackle this problem, our first effort is to characterize the local and global maxima by investi- gating the optimality conditions. Our results reveal that finding the global solution is closely related with a special extreme nonlinear eigenvalue problem, and in the spe- cial case D = μW (μ > 0), the set of the global solutions is essentially an eigenspace corresponding to the largest eigenvalue of a specially-defined matrix. The characteri- zation of the global solution not only sheds some lights on the maximization problem, but motives a starting point strategy to obtain the global maximizer for any monoton- ically convergent iteration. Our second part then realizes the Riemannian trust-region method of Absil, Baker and Gallivan (Found. Comput. Math. 7:303–330, 2007) into a practical algorithm to solve this problem, which enjoys the nice convergence prop- erties: global convergence and local superlinear convergence. Preliminary numerical tests are carried out and empirical evaluation of its performance is reported.

规划问题(1).pdf

本文档提供的代码是用Python写的，功能为通过遗传算法寻找双参数函数的极值，是一种优化算法。

简单的利用模拟退火算法求解函数f(x)=(x-2)^2+4的最小值，入门级程序，简单明了，适合单步调试，理解算法的运行机制

很浅显地对初等的极值问题作了一个总结.内容不超过初等微分学(最多就是Lagarange乘法).还有对近代极值问题的介绍.我个人推荐第四节:几何极值问题.

遗传算法是解决最优解的。其代码是java实现，且有main函数可以方便自行调试查看运行结果。

该资源利用粒子群优化算法解决了区间极值问题，该程序可运行，并且有良好的收敛效果，本程序来自老师课上讲解的书籍中，是一个典型的离散极值问题