function CONout = clean_up(CONin)% Remove all redundant constraints from a linear constraint object%% Syntax:%   "C = clean_up(a)"%% Description:%   "clean_up(a)" returns a linear constraint object representing the%   constraint set represented by "a" with all redundant constraints removed. %% Examples:%   Given a linear constraint object, "a" using six inequalities to%   represent the intersection of two squares in the x3 = 0 plane with%   corners at (x1,x2) pairs (2,1), (2,3), (4,3), and (4,1) and (2,1),%   (2,2), (3,1), and (3,2),  %%%%   "C = clean_up(a)"%%%%   returns "C", a linear constraint object which uses four inequalities%   to represent a square in the x3 = 0 plane with corners at (x1,x2)%pairs(2,1), (2,2), (3,2), and (3,1).%% See Also:%   linearcon,and,isfeasible% Since we are having at most one equality constraint for now,% we do nothing for equality constraintglobal GLOBAL_APPROX_PARAMglobal GLOBAL_OPTIM_PARbigM = GLOBAL_APPROX_PARAM.poly_bigM;epsilon = GLOBAL_APPROX_PARAM.poly_epsilon;% Check if new feasible inequality constraints are redundantCE = CONin.CE; dE = CONin.dE; NE = size(CE,1);CI = CONin.CI; dI = CONin.dI;done = 0;k = 1;while (k <= length(dI))  cIk = CI(k,:);  dIk = dI(k);  dIprime = dI;  dIprime(k) = dIk + bigM;  upperlim=ones(1,size(CI,2));  upperlim(k)=inf;  %xmax1 = lp(-cIk',[CE; CI],[dE; dIprime],[],[],[],NE);  %xmin1 = lp(cIk',[CE; CI],[dE; dIprime],[],[],[],NE);  xmax = linprog(-cIk',CI,dIprime,CE,dE,[],[],[],GLOBAL_OPTIM_PAR);  xmin = linprog( cIk',CI,dIprime,CE,dE,[],[],[],GLOBAL_OPTIM_PAR);  %if abs(xmin1-xmin)>epsilon |abs(xmax1-xmax)>epsilon   %	fprintf('Warning: lp and linprog are giving different results\n');  %   save diflp cIk CE CI dIprime dE options_linprog xmax1 xmin1 xmax xmin upperlim k  %   pause;  %end  old_diff = dIk - cIk*xmin;  new_diff = cIk*xmax - cIk*xmin;  if old_diff~=0     required = ((new_diff/old_diff) > (1+epsilon));  else     required=0;  end    % remove if redundant  if required    k = k + 1;  else    CI = [CI(1:k-1,:); CI(k+1:length(dI),:)];    dI = [dI(1:k-1); dI(k+1:length(dI))];  end    endif isempty(dI) | isempty(CI)  fprintf('Warning: empty inequality constraints\n')  CONout = linearcon;  else  CONout = linearcon(CE,dE,CI,dI);end