www.gusucode.com > SAE RBM 程序MATLAB源码代码实现的一个关于sae的例子 > minFunc/ArmijoBacktrack.m
function [t,x_new,f_new,g_new,funEvals,H] = ArmijoBacktrack(... x,t,d,f,fr,g,gtd,c1,LS,tolX,debug,doPlot,saveHessianComp,funObj,varargin) % % Backtracking linesearch to satisfy Armijo condition % % Inputs: % x: starting location % t: initial step size % d: descent direction % f: function value at starting location % fr: reference function value (usually funObj(x)) % gtd: directional derivative at starting location % c1: sufficient decrease parameter % debug: display debugging information % LS: type of interpolation % tolX: minimum allowable step length % doPlot: do a graphical display of interpolation % funObj: objective function % varargin: parameters of objective function % % Outputs: % t: step length % f_new: function value at x+t*d % g_new: gradient value at x+t*d % funEvals: number function evaluations performed by line search % H: Hessian at initial guess (only computed if requested % Evaluate the Objective and Gradient at the Initial Step if nargout == 6 [f_new,g_new,H] = feval(funObj, x + t*d, varargin{:}); else [f_new,g_new] = feval(funObj, x + t*d, varargin{:}); end funEvals = 1; while f_new > fr + c1*t*gtd || ~isLegal(f_new) temp = t; if LS == 0 || ~isLegal(f_new) % Backtrack w/ fixed backtracking rate if debug fprintf('Fixed BT\n'); end t = 0.5*t; elseif LS == 2 && isLegal(g_new) % Backtracking w/ cubic interpolation w/ derivative if debug fprintf('Grad-Cubic BT\n'); end t = polyinterp([0 f gtd; t f_new g_new'*d],doPlot); elseif funEvals < 2 || ~isLegal(f_prev) % Backtracking w/ quadratic interpolation (no derivative at new point) if debug fprintf('Quad BT\n'); end t = polyinterp([0 f gtd; t f_new sqrt(-1)],doPlot); else%if LS == 1 % Backtracking w/ cubic interpolation (no derivatives at new points) if debug fprintf('Cubic BT\n'); end t = polyinterp([0 f gtd; t f_new sqrt(-1); t_prev f_prev sqrt(-1)],doPlot); end % Adjust if change in t is too small/large if t < temp*1e-3 if debug fprintf('Interpolated Value Too Small, Adjusting\n'); end t = temp*1e-3; elseif t > temp*0.6 if debug fprintf('Interpolated Value Too Large, Adjusting\n'); end t = temp*0.6; end f_prev = f_new; t_prev = temp; if ~saveHessianComp && nargout == 6 [f_new,g_new,H] = feval(funObj, x + t*d, varargin{:}); else [f_new,g_new] = feval(funObj, x + t*d, varargin{:}); end funEvals = funEvals+1; % Check whether step size has become too small if sum(abs(t*d)) <= tolX if debug fprintf('Backtracking Line Search Failed\n'); end t = 0; f_new = f; g_new = g; break; end end % Evaluate Hessian at new point if nargout == 6 && funEvals > 1 && saveHessianComp [f_new,g_new,H] = feval(funObj, x + t*d, varargin{:}); funEvals = funEvals+1; end x_new = x + t*d; end