CAJ | 학술논문

谱共轭梯度法含有两个方向调控参数，是求解无约束优化问题的一类有效方法。本文给出一对参数公式以构建新的谱共轭梯度法，该方法在精确线搜索下与标准FR方法等价，在Wolfe线搜索下具有类似标准DY方法的内在性质。我们证明了采用Wolfe线搜索的新算法在每一次迭代中均产生下降方向，并且具有全局收敛性。数值实验结果表明，新算法数值稳定、有效，适合于求解大规模无约束优化问题。
보공액제도법함유량개방향조공삼수，시구해무약속우화문제적일류유효방법。본문급출일대삼수공식이구건신적보공액제도법，해방법재정학선수색하여표준FR방법등개，재Wolfe선수색하구유유사표준DY방법적내재성질。아문증명료채용Wolfe선수색적신산법재매일차질대중균산생하강방향，병차구유전국수렴성。수치실험결과표명，신산법수치은정、유효，괄합우구해대규모무약속우화문제。
Spectral conjugate gradient method contains two parameters for direction control, and it is a class of effective algorithms for unconstrained optimization problems. This paper presents a pair of formulas to create a new spectral conjugate gradient method, which is equiv-alent to the standard FR method when the line search is exact, and its intrinsic properties are similar to the standard DY method with Wolfe line search. The descent in each iteration and the global convergence of the new algorithm under Wolfe line search are proved. Preliminary numerical results show that the new algorithm is robust, effective and suitable for solving large-scale unconstrained optimization problems.