semivar.m

optimization toolbox

function varargout = semivar(varargin)
%SEMIVAR Create symbolic semicontinuous variable
%
%   SEMIVAR works exactly as SDPVAR, with the only difference that
%   the elements in the variable automatically will be constrained
%   to be semicontinous (x = 0 or |x| > 1)
%
%   See also SDPVAR, BINVAR, INTVAR, BINARY, INTEGER

% Author Johan L鰂berg
% $Id: semivar.m,v 1.2 2006/06/07 09:24:14 joloef Exp $

if isa(varargin{1},'char')
    switch varargin{1}
        case {'graph','milp'}
            t = varargin{2};
            d = binvar(3,1);
            [M,m] = derivebounds(t);
            % Zero case
            F = set(m.*(1-d(3)) < t < M.*(1-d(3)));
            % Special cases to speed up integer solve
            if M <=0
                F = F + set(t < -1+(M+1)*(1-d(2)));
                F = F + set(d(3) + d(2)==1);                
            elseif m>=0
                F = set(t >= 1+(1-d(1))*(m-1));
                F = F + set(d(3) + d(1)==1);                
            else
                F = set(t >= 1+(1-d(1))*(m-1)) + set(t < -1+(M+1)*(1-d(2)));
                F = F + set(m.*(1-d(3)) < t < M.*(1-d(3)));
                F = F + set(sum(d)==1);                
            end
            varargout{1} = F;
            varargout{2} = struct('convexity','milp','monotonicity','milp','definiteness','milp');
            varargout{3} = 1;
            return
        otherwise
            % Command line creation
            all_variable_names = 1;
            i = 1;
            while all_variable_names & i<=nargin
                all_variable_names = all_variable_names & isvarname(varargin{i});
                i = i + 1;
            end
            if all_variable_names
                for k = 1:nargin
                    varname = varargin{k};
                    assignin('caller',varname,semicont(1,1));
                end
                return
            end
    end
end

% Create dummy SDPVAR object
sys = sdpvar(varargin{:});
n = length(getvariables(sys));
% Create new variables
y = [];
for i = 1:n
    y = [y;yalmip('addextendedvariable',mfilename,rand)];
end
%  Replace variables to the semicontinous variables
varargout{1} = reshape(getbase(sys)*[1;y],size(sys,1),size(sys,2));