最速下降法与牛顿法及其区别.doc
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1、最速下降法与牛顿法及其区别摘要:无约束优化方法是优化技术中极为重要与根本内容之一。它不仅可以直接用来求解无约束优化问题,而且很多约束优化问题也常将其转化为无约束优化问题,然后用无约束优化方法来求解。最速下降法与牛顿法是比拟常见的求解无约束问题的最优化方法,这两种算法作为根本算法,在最优化方法中占有重要的地位。其中最速下降法又称梯度法,其优点是工作量少,存储变量较少,初始点要求不高;缺点是收敛慢,效率低。牛顿法的优点是收敛速度快;缺点是对初始点要求严格,方向构造困难,计算复杂且占用内存较大。同时,这两种算法的理论与方法渗透到许多方面,特别是在军事、经济、管理、生产过程自动化、工程设计与产品优化设
2、计等方面都有着重要的应用。因此,研究最速下降法与牛顿法的原理及其算法对我们有着及其重要的意义。关键字:无约束优化 最速下降法 牛顿法 Abstract: unconstrained optimization method is to optimize the technology is extremely important and basic content of. It not only can be directly used to solve unconstrained optimization problems, and a lot of constrained optimizati
3、on problems are often transformed into unconstrained optimization problem, and then use the unconstrained optimization methods to solve. The steepest descent method and Newton-Raphson method is relatively common in the unconstrained problem optimization method, these two kinds of algorithm as the ba
4、sic algorithm, the optimization method plays an important role in. One of the steepest descent method also known as gradient method, its advantages are less workload, storage variable is less, the initial requirements is not high; drawback is the slow convergence, low efficiency. Newtonian method ha
5、s the advantages of fast convergence speed; drawback is the initial point of strict construction difficulties, directions, complicated calculation and larger memory. At the same time, these two kinds of algorithm theory and methods into many aspects, especially in the military, economic, management,
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