CAJ | 학술논문

尝试在有限存储类算法中利用目标函数值所提供的信息.首先利用插值条件构造了一个新的二次函数逼近目标函数,得到了一个新的弱割线方程,然后将此弱割线方程与袁[1]的弱割线方程相结合,给出了一族包括标准LBFGS的有限存储BFGS类算法,证明了这族算法的收敛性.从标准试验函数库CUTE中选择试验函数进行了数值试验,试验结果表明这族算法的数值表现都与标准LBFGS类似.
상시재유한존저류산법중이용목표함수치소제공적신식.수선이용삽치조건구조료일개신적이차함수핍근목표함수,득도료일개신적약할선방정,연후장차약할선방정여원[1]적약할선방정상결합,급출료일족포괄표준LBFGS적유한존저BFGS류산법,증명료저족산법적수렴성.종표준시험함수고CUTE중선택시험함수진행료수치시험,시험결과표명저족산법적수치표현도여표준LBFGS유사.
In this paper,value information of objective function is exploited in limited memory BFGS-type algorithms.We first construct a new quadratic function satisfying some interpolation conditions to approximate the objective function,and get a new weak secant equation.Combining the new weak secant equation with that obtained by Yuan[1],a class of limited memory BFGS-type algorithms including the classic LBFGS algorithm based on a new weak secant equation is proposed.The convergence of this class limited memory BFGS-type algorithms is proved.Numerical results for standard test problems from CUTE are reported,which indicate that all the algorithms in the proposed class perform quite well.