非线性边界和等式约束条件下的高维函数优化算法研究

本文建立了基于模式搜索法的非线性边界约束条件下多参数函数的优化算法。通过综合模式搜索法、最速下降法和转轴法解决了在高维空间中的优化算法和非线性边界约束的算法问题。同时使用广义拉格朗日乘子法解决了非线性等式约束条件的计算方法。通过在四轨道隶玻色子模型计算中的应用，验证了该计算方法的有效性。由于该方法综合了多种经典优化算法，因此可以广泛适用于在非线性复杂边界约束条件下的多参数函数的优化计算。

Numerical Algorithm for High-Dimensional Optimization with Nonlinear Boundary and Equality Constrains

In this paper, an optimization method for high-dimensional functions with nonlinear boundary constrain is presented. The method is mainly based on pattern research method combining with Steepest Descent Method and Rosenbrock method. The nonlinear equality constrains are treated with generalized Lagrange multiplier method. It has been successfully applied to the slave boson approach for four orbital Hubbard model, and it is shown the validity of our numerical method. Since many classical optimization methods are integrated in our method, we believe that it can be used for a wide range of optimization problems of high dimensional function with complex boundary constrains.