求解单变量无约束优化问题的一类新割线法(英文)

New Secant-Type Methods for Univariate Unconstrained Optimization

本文基于分式逼近提出了一类求解单变量无约束优化问题的新割线法,给出并证明了该方法的收敛阶是(^(1/2)+1).并进一步对新方法的性能进行了分析,给出了新方法、经典的牛顿法和其他修正的割线类方法解单变量无约束优化问题的数值实验.理论和数值结果均表明新的割线法是有效的.

This paper presents a class of new secant methods for solving nonlinear, univariate and unconstrained optimization problems based on the fractional approximation. Convergence analysis shows the proposed methods to be （√2＋ 1）-order convergent. The performance of the new methods is analyzed. In comparison with the classical Newton method and modified secant-type methods, numerical results indicate that new proposed methods are effective.