应用数学
應用數學
응용수학
MATHEMATICA APPLICATA
2012年
1期
202-208
,共7页
大规模无约束优化%梯度方法%非单调线搜索
大規模無約束優化%梯度方法%非單調線搜索
대규모무약속우화%제도방법%비단조선수색
Large scale unconstrained optimization%Gradient method%Nonmonotone line search
本文提出一种新的解大规模无约束优化问题的全局收敛的梯度法.新算法沿着负梯度方向选择步长,而初始步长根据目标函数的海赛矩阵的近似数量矩阵来确定.理论上证明了新算法产生的点列的每个聚点都是稳定的,数值试验表明新算法是可靠且有效的.
本文提齣一種新的解大規模無約束優化問題的全跼收斂的梯度法.新算法沿著負梯度方嚮選擇步長,而初始步長根據目標函數的海賽矩陣的近似數量矩陣來確定.理論上證明瞭新算法產生的點列的每箇聚點都是穩定的,數值試驗錶明新算法是可靠且有效的.
본문제출일충신적해대규모무약속우화문제적전국수렴적제도법.신산법연착부제도방향선택보장,이초시보장근거목표함수적해새구진적근사수량구진래학정.이론상증명료신산법산생적점렬적매개취점도시은정적,수치시험표명신산법시가고차유효적.
In this paper,a nonmonotone gradient method for large scale unconstrained optimization is proposed.The new algorithm selects the steplength along the negative gradient direction and the initial stepsize is determined using a new scale approximation of the minimizing function's Hessian.Every limit point of the sequence generated by the new algorithm is proved to be a stationary point of the objective function.Numerical tests on a set of large scale standard test problems are presented and show that the new algorithm is efficient and robust.