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研究有不等式约束的非线性规划问题,构造了一种新的两阶段算法:(1)利用传统优化方法求出原问题的一个局部极小点x*;(2)基于当前局部极小点和“准”罚函数的思想构造了一个辅助函数,该辅助函数连续可微、有界并且是凸的,该函数的局部极小点y*很容易求得,并且y*位于比x*更低的盆域中,从而y*可以作为第一阶段中的初始点,从而找到另一个更好的局部极小点.两个阶段不断循环,只要原问题具有有限个局部极小点,就可以找到它的全局极小点.为了测试算法的性能,对几个测试问题进行了求解.结果表明算法有效的,可以快捷的跳出局部极小点达到全局极小点.
A new two-stage algorithm is proposed to study the nonlinear programming problem with inequality constraints: (1) a local minimum x * of the original problem is obtained by the traditional optimization method; (2) Based on the current local minimum and “Quasi ” penalty function constructs a helper function, the auxiliary function continuously differentiable, bounded and convex, the function of the local minimum y * is easy to find, and y * is located in the x * Lower basin, so that y * can be used as the initial point in the first stage to find another better local minimum point. The two stages are constantly cycling, as long as the original problem has a finite number of local minimum points We can find its global minimum.In order to test the performance of the algorithm, several test problems are solved.The results show that the algorithm is effective and can jump out of the local minimum to reach the global minimum.