用变换函数解带线性约束的全局最优问题

Transformed Function Method for Global Optimization with Linear Constraints

结合变换函数方法和下降算法对目标函数有多个极值点且带有线性约束的非线性规划全局问题提出算法.使用的变换函数兼具填充函数和打洞函数的特点.在理论上证明如果当前局部极小点不是全局最优解,一定存在一个变换函数的极小点使得该点的目标函数值小于当前局部极小点的函数值,且该点位于原问题的可行域内.以此点为初始点求解原问题可得到更好的局部极小点.

Based on the transformed function method and descent method, an algorithm is presented for constraint global optimizations with the multi-extremum objective function. The transformed functions have both the characters of filled functions and tunnelling functions. It is theoretically proved that if the current minimizer is not a global one, there must exist a transformed function＇s minimizer in the feasible region so that the objective value is less than the current value. A better minimizer can be obtained in solving the primal problem with the minimizer of transformed function assumed to be an initial point in descent process.