一种新的混合共轭梯度法及其在投资组合中的应用

A New Hybrid Conjugate Gradient Method and Its Application in Investment Portfolio

考虑无约束优化问题,在不同维数的空间上获得具有充分下降性的搜索方向,进而提出一个新的混合共轭梯度方法,在梯度Lipschitz连续条件下,证明了算法的全局收敛性。数值实验表明,该算法具有一定竞争力,将该方法应用于求解Markowitz投资组合问题,得到不同收益率下的投资组合策略。

We consider the unconstrained optimization,obtain the search direction with sufficient descent in the space of different dimensions,and then propose a new hybrid conjugate gradient method,which proves the global convergence of the algorithm under the continuous gradient Lipschitz condition.Numerical experiments show that the algorithm is competitive,the method is applied to solve Markowitz investment portfolio to obtain portfolio strategies with different yields.