【摘要】 若假设F:R~n→R~n是局部Lipschitz连续且半光滑的,讨论了求解不可微方程F(x)=0的PSB方法与DFP方法的q-线性收敛性。若更进一步假设F(x)在解x~*处是B可微的(即BF(x~*)存在),且BF(x~*)对称非奇异(对DFP方法还需假设BF(x~*)正定),还证明了PSB方法及DFP方法的q~-超线性收敛性。更多还原

【Abstract】 If the function F:Rn→Rn is local Lipschitz continuous and semi-smooth, q-linear convergence of PSB and DFP methods form solving non-differentiable equation F(x) =0 is discussed. Furthermore, if F(x) is B -differentiable at a solution x * of F(x) =0 and BF(x* ) is symmetric nonsingular (BF(x* ) is symmetric positive definite for DFP method), q-superlinear convergence is proven for PSB and DFP methods.更多还原