- 作者: 朱亮儒
- 作者服務機構: 台灣師範大學數學系
- 中文摘要: 本文描述一個解非線性方程式(nonlinear equation)OE T(x)的偏近位點法(partial proximal point algorithm),其中T為積Hilbert空問H:=H1xH2中的極大單調多值函數(maximal monotone multifunction)。在限制條件OE int(coR(T))之下,我們證明此種偏近位點法與傳統的近位點法有類似的收瀲性質。此外,我們也進一步分析與估計其收斂率( convergence rate)。
- 英文摘要: We analyze asymptotic convergence of the partial proximal point algorithm to solve the generalizednonlinear equation OE T(x), where T:H→H is a maximal monotone multifunction and H:=H xH , a productof two real Hilbert spaces. Under the mild feasibility assumption 0E int(co R(T)), we prove that the partialproximal point algorithm has the same convergence properties as does the regular proximal point algorithmgiven by Rockafellar(1976a). Moreover, the partial convergence rates are shown to depend upon howrapidly T-' grows away from the solution set T (0) in a neighborhood of 0. When the growth is Lipschitzcontinuous at 0, then for any t in (0, 1)the partial convergence rate estimate is O(t").When T satisfiesa partial growth property of order s, the partial convergence rate estimate is (方程式無法摘錄) .
- 中文關鍵字: maximal monotone multifications; xonvex programming; proximal point algorithm; non-linear equations; rate of convergence
- 英文關鍵字: --