63 lines
1.8 KiB
Mathematica
63 lines
1.8 KiB
Mathematica
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function varargout = hinge(varargin)
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%HINGE Models convex operator max(0,x^p) for integer p>=1
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%
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% t = hinge(x,p)
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switch class(varargin{1})
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case 'double'
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if nargin == 1
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varargout{1} = max(0,varargin{1});
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else
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varargout{1} = max(0,varargin{1}.^varargin{2});
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end
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case 'sdpvar' % Overloaded operator for SDPVAR objects. Pass on args and save them.
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X = varargin{1};
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if nargin == 1
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p = 2;
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else
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p = varargin{2};
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end
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if p <= 1
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error('HINGE max(0,x^p) must have p>=1')
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elseif ~(p==ceil(p))
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error('HINGE max(0,x^p) must have integer p')
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elseif p == 1
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varargout{1} = max(0,X);
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else
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varargout{1} = yalmip('define',mfilename,X,p);
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end
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case 'char' % YALMIP send 'model' when it wants the epigraph or hypograph
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if isequal(varargin{1},'graph')
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t = varargin{2}; % Second arg is the extended operator variable
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X = varargin{3}; % Third arg and above are the args user used when defining t.
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p = varargin{4};
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convexity = 'convex';
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if ~even(p)
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monotonicity = 'increasing';
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else
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monotonicity = 'none';
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end
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e = sdpvar(1);
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F = [e >= X, pospower(e,t,p)];
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varargout{1} = F;
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varargout{2} = struct('convexity',convexity,'monotonicity',monotonicity,'definiteness','positive','model','graph');
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varargout{3} = X;
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end
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otherwise
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end
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function F = pospower(x,t,p)
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q = 1;
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l = ceil(log2(abs(p)));
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r = 2^l-p;
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y = [ones(r,1)*x;ones(q,1)*t;ones(2^l-r-q,1)];
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F = detset(x,y);
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