function lambdap = parab3p(lambdac, lambdam, ff0, ffc, ffm) % Apply three-point safeguarded parabolic model for a line search. % % C. T. Kelley, June 29, 1994 % % This code comes with no guarantee or warranty of any kind. % % function lambdap = parab3p(lambdac, lambdam, ff0, ffc, ffm) % % input: % lambdac = current steplength % lambdam = previous steplength % ff0 = value of \| F(x_c) \|^2 % ffc = value of \| F(x_c + \lambdac d) \|^2 % ffm = value of \| F(x_c + \lambdam d) \|^2 % % output: % lambdap = new value of lambda given parabolic model % % internal parameters: % sigma0 = .1, sigma1=.5, safeguarding bounds for the linesearch % % % set internal parameters % sigma0=.1; sigma1=.5; % % compute coefficients of interpolation polynomial % % p(lambda) = ff0 + (c1 lambda + c2 lambda^2)/d1 % % d1 = (lambdac - lambdam)*lambdac*lambdam < 0 % so if c2 > 0 we have negative curvature and default to % lambdap = sigam1 * lambda % c2 = lambdam*(ffc-ff0)-lambdac*(ffm-ff0); if c2 >= 0 lambdap = sigma1*lambdac; return end c1=lambdac*lambdac*(ffm-ff0)-lambdam*lambdam*(ffc-ff0); lambdap=-c1*.5/c2; if (lambdap < sigma0*lambdac) lambdap=sigma0*lambdac; end if (lambdap > sigma1*lambdac) lambdap=sigma1*lambdac; end