【摘要】 本文讨论一般的凸光顺问题minF（y）:=integral from n=a to b|D^k y|² dt+sum from i=1 to N wⁱ|y（tⁱ）-zⁱ|².其中,k≥3而且y在闭凸集K■L₂^k[a,b]上.我们把该问题转化为半光滑方程组并给出一个求解该方程组的半光滑牛顿算法.最后证明算法的超线性收敛性并给出数值算例.更多还原

【Abstract】 In this paper we discuss the general convex smoothing problem: minimize F(y):=(?).where k≥3 and y is in a closed convex set K(?)L2k[a,b]. We reduce the problem to a system of semismooth equations and propose a semismooth Newton algorithm for the system. The superlinear convergence of the algorithm is proved and some numerical results are reported.更多还原