43 lines
998 B
Mathematica
43 lines
998 B
Mathematica
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function [Ax,Ay,b,K] = convexhullConcave(varargin)
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%function [Ax,Ay,b] = convexhullConcave(xL,xU,fL,fU,dfL,dfU)
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% Two lower bounds from tangents
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% y < f(xL) + (x-xL)*df(xL)
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% y < f(xU) + (x-xL)*df(xU)
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% Upper bound from conneting extreme points
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% y > f(xU)(x-xL)/(xU-xL) + f(xL)(xU-x)/(xU-xL)
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% can be wrtitten as
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% Ax*x + Ay*y < b
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if rem(nargin,3)
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error('The convex hull generator assumes n triplets (x,f,df).')
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end
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m = nargin/3;
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x = [varargin{(1:m)}]';
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f = [varargin{(1:m)+m}]';
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df = [varargin{(1:m)+2*m}]';
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if all(diff(x)>0)
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Ay = -[-ones(m,1);1];
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b = [f - x.*df; f(end)*x(1)/(x(end)-x(1)) - f(1)*x(end)/(x(end)-x(1))];
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Ax = [-df;f(end)/(x(end)-x(1)) - f(1)/(x(end)-x(1))];
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% Don't use ill-conditioned cuts
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if df(1)>1000
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Ax(1)=[];
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Ay(1) = [];
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b(1) = [];
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end
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if df(end)<-1000
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Ax(end)=[];
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Ay(end) = [];
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b(end) = [];
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end
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else
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Ax = [];
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Ay = [];
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b = [];
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end
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K.f = 0;
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K.l = length(b);
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