jens
7b34529b24
git-svn-id: http://moon:8086/svn/matlab/trunk@91 801c6759-fa7c-4059-a304-17956f83a07c
140 lines
4.4 KiB
Matlab
140 lines
4.4 KiB
Matlab
function [t,x_new,f_new,g_new,funEvals,H] = ArmijoBacktrack(...
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x,t,d,f,fr,g,gtd,c1,LS_interp,LS_multi,progTol,debug,doPlot,saveHessianComp,funObj,varargin)
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% [t,x_new,f_new,g_new,funEvals,H] = ArmijoBacktrack(...
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% x,t,d,f,fr,g,gtd,c1,LS_interp,LS_multi,progTol,debug,doPlot,saveHessianComp,funObj,varargin)
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%
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% Backtracking linesearch to satisfy Armijo condition
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%
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% Inputs:
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% x: starting location
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% t: initial step size
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% d: descent direction
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% f: function value at starting location
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% fr: reference function value (usually funObj(x))
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% gtd: directional derivative at starting location
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% c1: sufficient decrease parameter
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% debug: display debugging information
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% LS_interp: type of interpolation
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% progTol: minimum allowable step length
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% doPlot: do a graphical display of interpolation
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% funObj: objective function
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% varargin: parameters of objective function
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%
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% Outputs:
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% t: step length
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% f_new: function value at x+t*d
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% g_new: gradient value at x+t*d
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% funEvals: number function evaluations performed by line search
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% H: Hessian at initial guess (only computed if requested)
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%
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% recet change: LS changed to LS_interp and LS_multi
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% Evaluate the Objective and Gradient at the Initial Step
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if nargout == 6
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[f_new,g_new,H] = funObj(x + t*d,varargin{:});
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else
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[f_new,g_new] = funObj(x+t*d,varargin{:});
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end
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funEvals = 1;
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while f_new > fr + c1*t*gtd || ~isLegal(f_new)
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temp = t;
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if LS_interp == 0 || ~isLegal(f_new)
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% Ignore value of new point
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if debug
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fprintf('Fixed BT\n');
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end
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t = 0.5*t;
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elseif LS_interp == 1 || ~isLegal(g_new)
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% Use function value at new point, but not its derivative
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if funEvals < 2 || LS_multi == 0 || ~isLegal(f_prev)
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% Backtracking w/ quadratic interpolation based on two points
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if debug
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fprintf('Quad BT\n');
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end
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t = polyinterp([0 f gtd; t f_new sqrt(-1)],doPlot,0,t);
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else
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% Backtracking w/ cubic interpolation based on three points
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if debug
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fprintf('Cubic BT\n');
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end
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t = polyinterp([0 f gtd; t f_new sqrt(-1); t_prev f_prev sqrt(-1)],doPlot,0,t);
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end
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else
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% Use function value and derivative at new point
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if funEvals < 2 || LS_multi == 0 || ~isLegal(f_prev)
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% Backtracking w/ cubic interpolation w/ derivative
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if debug
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fprintf('Grad-Cubic BT\n');
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end
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t = polyinterp([0 f gtd; t f_new g_new'*d],doPlot,0,t);
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elseif ~isLegal(g_prev)
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% Backtracking w/ quartic interpolation 3 points and derivative
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% of two
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if debug
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fprintf('Grad-Quartic BT\n');
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end
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t = polyinterp([0 f gtd; t f_new g_new'*d; t_prev f_prev sqrt(-1)],doPlot,0,t);
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else
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% Backtracking w/ quintic interpolation of 3 points and derivative
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% of two
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if debug
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fprintf('Grad-Quintic BT\n');
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end
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t = polyinterp([0 f gtd; t f_new g_new'*d; t_prev f_prev g_prev'*d],doPlot,0,t);
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end
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end
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% Adjust if change in t is too small/large
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if t < temp*1e-3
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if debug
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fprintf('Interpolated Value Too Small, Adjusting\n');
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end
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t = temp*1e-3;
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elseif t > temp*0.6
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if debug
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fprintf('Interpolated Value Too Large, Adjusting\n');
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end
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t = temp*0.6;
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end
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% Store old point if doing three-point interpolation
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if LS_multi
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f_prev = f_new;
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t_prev = temp;
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if LS_interp == 2
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g_prev = g_new;
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end
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end
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if ~saveHessianComp && nargout == 6
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[f_new,g_new,H] = funObj(x + t*d,varargin{:});
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else
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[f_new,g_new] = funObj(x + t*d,varargin{:});
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end
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funEvals = funEvals+1;
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% Check whether step size has become too small
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if max(abs(t*d)) <= progTol
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if debug
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fprintf('Backtracking Line Search Failed\n');
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end
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t = 0;
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f_new = f;
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g_new = g;
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break;
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end
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end
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% Evaluate Hessian at new point
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if nargout == 6 && funEvals > 1 && saveHessianComp
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[f_new,g_new,H] = funObj(x + t*d,varargin{:});
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funEvals = funEvals+1;
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end
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x_new = x + t*d;
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end
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