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HSDsqlpmain.m
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%%*****************************************************************************
%% HSDsqlp: solve an semidefinite-quadratic-linear program
%% by infeasible path-following method on the homogeneous self-dual model.
%%
%% [obj,X,y,Z,info,runhist] =
%% HSDsqlp(blk,At,C,b,OPTIONS,X0,y0,Z0,kap0,tau0,theta0);
%%
%% Input:
%% blk : a cell array describing the block diagonal structure of SQL data.
%% At : a cell array with At{p} = [svec(Ap1) ... svec(Apm)]
%% b,C : data for the SQL instance.
%% OPTIONS: a structure that specifies parameters required in HSDsqlp.m,
%% (if it is not given, the default in sqlparameters.m is used).
%%
%% (X0,y0,Z0): an initial iterate (if it is not given, the default is used).
%% (kap0,tau0,theta0): initial parameters (if not given, the default is used).
%%
%% Output: obj = [<C,X> <b,y>].
%% (X,y,Z): an approximately optimal solution or a primal or dual
%% infeasibility certificate.
%% info.termcode = termination-code
%% info.iter = number of iterations
%% info.obj = [primal-obj, dual-obj]
%% info.cputime = total-time
%% info.gap = gap
%% info.pinfeas = primal_infeas
%% info.dinfeas = dual_infeas
%% runhist.pobj = history of primal objective value.
%% runhist.dobj = history of dual objective value.
%% runhist.gap = history of <X,Z>.
%% runhist.pinfeas = history of primal infeasibility.
%% runhist.dinfeas = history of dual infeasibility.
%% runhist.cputime = history of cputime spent.
%%----------------------------------------------------------------------------
%% The OPTIONS structure specifies the required parameters:
%% vers gam predcorr expon gaptol inftol steptol
%% maxit printlevel ...
%% (all have default values set in sqlparameters.m).
%%
%%*************************************************************************
%% SDPT3: version 3.1
%% Copyright (c) 1997 by
%% K.C. Toh, M.J. Todd, R.H. Tutuncu
%% Last Modified: 16 Sep 2004
%%*************************************************************************
function [obj,X,y,Z,info,runhist] = ...
HSDsqlpmain(blk,At,C,b,par,X0,y0,Z0,kap0,tau0,theta0)
%%
%%-----------------------------------------
%% get parameters from the OPTIONS structure.
%%-----------------------------------------
%%
global spdensity smallblkdim solve_ok use_LU
global schurfun schurfun_par
%%
randstate = rand('state'); randnstate = randn('state'); %#ok
rand('state',0); randn('state',0); %#ok
%%
% matlabversion = par.matlabversion;
vers = par.vers;
predcorr = par.predcorr;
gam = par.gam;
expon = par.expon;
gaptol = par.gaptol;
inftol = par.inftol;
steptol = par.steptol;
maxit = par.maxit;
printlevel = par.printlevel;
stoplevel = par.stoplevel;
% scale_data = par.scale_data;
spdensity = par.spdensity;
rmdepconstr = par.rmdepconstr;
smallblkdim = par.smallblkdim;
schurfun = par.schurfun;
schurfun_par = par.schurfun_par;
% ublksize = par.ublksize;
%%
tstart = clock;
X = X0; y = y0; Z = Z0;
for p = 1:size(blk,1)
if strcmp(blk{p,1},'u'); Z{p} = zeros(blk{p,2},1); end
end
%%
%%-----------------------------------------
%% convert unrestricted blk to linear blk.
%%-----------------------------------------
%%
ublkidx = zeros(size(blk,1),1);
Cpert = zeros(size(blk,1),1);
Cnew = C;
perturb_C = 1;
for p = 1:size(blk,1)
pblk = blk(p,:);
n = sum(pblk{2});
tmp = max(1,norm(C{p},'fro'))/sqrt(n);
if strcmp(pblk{1},'s')
if (perturb_C); Cpert(p) = 1e-3*tmp; end
Cnew{p} = C{p} + Cpert(p)*speye(n);
elseif strcmp(pblk{1},'q')
if (perturb_C); Cpert(p) = 0*tmp; end; %% old: 1e-3
s = 1+[0, cumsum(pblk{2})];
tmp2 = zeros(n,1); len = length(pblk{2});
tmp2(s(1:len)) = ones(len,1);
Cnew{p} = C{p} + Cpert(p)*tmp2;
elseif strcmp(pblk{1},'l')
if (perturb_C); Cpert(p) = 1e-4*tmp; end; %% old: 1e-3
Cnew{p} = C{p} + Cpert(p)*ones(n,1);
elseif strcmp(pblk{1},'u')
msg = sprintf('convert ublk to linear blk');
if (printlevel); fprintf('\n *** %s',msg); end
ublkidx(p) = 1;
n = 2*pblk{2};
blk{p,1} = 'l'; blk{p,2} = n;
if (perturb_C); Cpert(p) = 1e-2*tmp; end
C{p} = [C{p}; -C{p}];
At{p} = [At{p}; -At{p}];
Cnew{p} = C{p} + Cpert(p)*ones(n,1);
X{p} = 1+rand(n,1); %% do not add a factor of n
Z{p} = 1+rand(n,1); %%
end
end
%%
%%-----------------------------------------
%% check if the matrices Ak are
%% linearly independent.
%%-----------------------------------------
%%
m0 = length(b);
[At,b,y,indeprows,depconstr,feasible,AAt] = ...
checkdepconstr(blk,At,b,y,rmdepconstr);
if (~feasible)
msg = 'SQLP is not feasible';
if (printlevel); fprintf('\n %s',msg); end
return;
end
par.depconstr = depconstr;
%%
normb = 1+max(abs(b));
normC = zeros(length(C),1);
for p = 1:length(C); normC(p) = max(max(abs(C{p}))); end
normC = 1+max(normC);
nn = ops(C,'getM');
m = length(b);
if (nargin <= 8) || (isempty(kap0) || isempty(tau0) || isempty(theta0))
if (max([ops(At,'norm'),ops(C,'norm'),norm(b)]) > 1e6)
kap0 = 10*blktrace(blk,X,Z);
else
kap0 = blktrace(blk,X,Z);
end
tau0 = 1; theta0 = 1;
end
kap = kap0; tau = tau0; theta = theta0;
%%
normX0 = ops(X0,'norm')/tau; normZ0 = ops(Z0,'norm')/tau;
bbar = (tau*b-AXfun(blk,At,[],X))/theta;
ZpATy = ops(Z,'+',Atyfun(blk,At,[],[],y));
Cbar = ops(ops(ops(tau,'*',C),'-',ZpATy),'/',theta);
gbar = (blktrace(blk,C,X)-b'*y+kap)/theta;
abar = (blktrace(blk,X,Z)+tau*kap)/theta;
for p = 1:size(blk,1);
pblk = blk(p,:);
if strcmp(pblk{1},'s')
At{p} = [At{p}, -svec(pblk,Cnew{p},1), svec(pblk,Cbar{p},1)];
else
At{p} = [At{p}, -Cnew{p}, Cbar{p}];
end
end
Bmat = [sparse(m,m), -b, bbar; b', 0, gbar; -bbar', -gbar, 0];
em1 = zeros(m+2,1); em1(m+1) = 1;
em2 = zeros(m+2,1); em2(m+2) = 1;
par.Umat = [[b;0;0], [bbar;gbar;0], em1, em2];
par.m = m;
par.diagAAt = [full(diag(AAt)); 1; 1];
%%
%%-----------------------------------------
%% find the combined list of non-zero
%% elements of Aj, j = 1:k, for each k.
%%-----------------------------------------
%%
par.numcolAt = length(b)+2;
[At,C,Cnew,X,Z,par.permA,par.invpermA,par.permZ] = ...
HSDsortA(blk,At,C,Cnew,[b;0;0],X,Z); %#ok
[par.isspA,par.nzlistA,par.nzlistAsum,par.isspAy,par.nzlistAy] = ...
nzlist(blk,At,par);
%%
%%-----------------------------------------
%% initialization
%%-----------------------------------------
%%
y2 = [y; tau; theta];
AX = AXfun(blk,At,par.permA,X);
rp = [zeros(m,1); kap; -abar] - AX - Bmat*y2;
% Rd = ops(Atyfun(blk,At,par.permA,par.isspAy,-y2),'-',Z);
trXZ = blktrace(blk,X,Z);
mu = (trXZ+kap*tau)/(nn+1);
obj = [blktrace(blk,C,X), b'*y]/tau;
gap = trXZ/tau^2;
relgap = gap/(1+mean(abs(obj)));
ZpATy = ops(Z,'+',Atyfun(blk,At,par.permA,par.isspAy,[y;0;0]));
ZpATynorm = ops(ZpATy,'norm');
prim_infeas = norm(b - AX(1:m)/tau)/normb;
dual_infeas = ops(ops(C,'-',ops(ZpATy,'/',tau)),'norm')/normC;
infeas = max(prim_infeas,dual_infeas);
%%
termcode = 0;
pstep = 1; dstep = 1; pred_convg_rate = 1; corr_convg_rate = 1;
prim_infeas_best = prim_infeas;
dual_infeas_best = dual_infeas;
infeas_best = infeas;
relgap_best = relgap;
% homRd = inf; homrp = inf; dy = zeros(length(b),1);
msg = []; msg2 = [];
runhist.pobj = obj(1);
runhist.dobj = obj(2);
runhist.gap = gap;
runhist.relgap = relgap;
runhist.pinfeas = prim_infeas;
runhist.dinfeas = dual_infeas;
runhist.infeas = infeas;
runhist.cputime = etime(clock,tstart);
runhist.step = 0;
runhist.kappa = kap;
runhist.tau = tau;
runhist.theta = theta;
runhist.useLU = 0;
ttime.preproc = runhist.cputime;
ttime.pred = 0; ttime.pred_pstep = 0; ttime.pred_dstep = 0;
ttime.corr = 0; ttime.corr_pstep = 0; ttime.corr_dstep = 0;
ttime.pchol = 0; ttime.dchol = 0; ttime.misc = 0;
%%
%%-----------------------------------------
%% display parameters, and initial info
%%-----------------------------------------
%%
if (printlevel >= 2)
fprintf('\n********************************************');
fprintf('************************************************\n');
fprintf(' SDPT3: homogeneous self-dual path-following algorithms');
fprintf('\n********************************************');
fprintf('************************************************\n');
[hh,mm,ss] = mytime(ttime.preproc);
if (printlevel>=3)
fprintf(' version predcorr gam expon\n');
if (vers == 1); fprintf(' HKM '); elseif (vers == 2); fprintf(' NT '); end
fprintf(' %1.0f %4.3f %1.0f\n',predcorr,gam,expon);
fprintf('it pstep dstep pinfeas dinfeas gap')
fprintf(' mean(obj) cputime kap tau theta\n');
fprintf('------------------------------------------------');
fprintf('--------------------------------------------\n');
fprintf('%2.0f|%4.3f|%4.3f|%2.1e|%2.1e|',0,0,0,prim_infeas,dual_infeas);
fprintf('%2.1e|%- 7.6e| %s:%s:%s|',gap,mean(obj),hh,mm,ss);
fprintf('%2.1e|%2.1e|%2.1e|',kap,tau,theta);
end
end
%%
%%---------------------------------------------------------------
%% start main loop
%%---------------------------------------------------------------
%%
EE = ops(blk,'identity');
normE = ops(EE,'norm');
Zpertold = 1;
[Xchol,indef(1)] = blkcholfun(blk,X);
[Zchol,indef(2)] = blkcholfun(blk,Z);
if any(indef)
msg = 'stop: X, Z are not both positive definite';
if (printlevel); fprintf('\n %s\n',msg); end
info.termcode = -3;
info.msg1 = msg;
return;
end
%%
param.termcode = termcode;
param.iter = 0;
param.normX0 = normX0;
param.normZ0 = normZ0;
param.m0 = m0;
param.indeprows = indeprows;
param.prim_infeas_bad = 0;
param.dual_infeas_bad = 0;
param.prim_infeas_min = prim_infeas;
param.dual_infeas_min = dual_infeas;
param.gaptol = gaptol;
param.inftol = inftol;
param.maxit = maxit;
param.printlevel = printlevel;
param.stoplevel = stoplevel;
breakyes = 0;
dy = zeros(length(b),1); dtau = 0; dtheta = 0;
Xbest = X; ybest = y; Zbest = Z;
% kapbest = kap; taubest = tau; thetabest = theta;
%%
for iter = 1:maxit;
update_iter = 0; pred_slow = 0; corr_slow = 0; % step_short = 0;
tstart = clock;
timeold = tstart;
par.kap = kap;
par.tau = tau;
par.theta = theta;
par.mu = mu;
par.iter = iter;
par.y = y;
par.dy2 = [dy; dtau; dtheta];
par.rp = rp;
par.ZpATynorm = ZpATynorm;
%%
%%--------------------------------------------------
%% perturb C
%%--------------------------------------------------
%%
if (perturb_C)
[At,Cpert] = HSDsqlpCpert(blk,At,par,C,X,Cpert,runhist);
maxCpert(iter) = max(Cpert); %#ok
%%fprintf(' %2.1e',max(Cpert));
if (iter > 10 && norm(diff(maxCpert([iter-3,iter]))) < 1e-13)
Cpert = 0.5*Cpert;
maxCpert(iter) = max(Cpert); %#ok
end
AX = AXfun(blk,At,par.permA,X);
rp = [zeros(m,1); kap; -abar] - AX - Bmat*y2;
Rd = ops(Atyfun(blk,At,par.permA,par.isspAy,-y2),'-',Z);
end
%%---------------------------------------------------------------
%% predictor step.
%%---------------------------------------------------------------
%%
if (predcorr)
sigma = 0;
else
sigma = 1-0.9*min(pstep,dstep);
if (iter == 1); sigma = 0.5; end;
end
sigmu = sigma*mu;
invXchol = cell(size(blk,1),1);
invZchol = ops(Zchol,'inv');
if (vers == 1);
[par,dX,dy,dZ,coeff,L,hRd] = ...
HSDHKMpred(blk,At,par,rp,Rd,sigmu,X,Z,invZchol);
elseif (vers == 2);
[par,dX,dy,dZ,coeff,L,hRd] = ...
HSDNTpred(blk,At,par,rp,Rd,sigmu,X,Z,Zchol,invZchol);
end
if (solve_ok <= 0)
msg = 'stop: difficulty in computing predictor directions';
if (printlevel); fprintf('\n %s',msg); end
runhist.cputime(iter+1) = etime(clock,tstart);
termcode = -4;
break;
end
timenew = clock;
ttime.pred = ttime.pred + etime(timenew,timeold); timeold=timenew;
%%
%%-----------------------------------------
%% step-lengths for predictor step
%%-----------------------------------------
%%
if (gam == 0)
gamused = 0.9 + 0.09*min(pstep,dstep);
else
gamused = gam;
end
kapstep = max( (par.dkap<0)*(-kap/(par.dkap-eps)), (par.dkap>=0)*1e6 );
taustep = max( (par.dtau<0)*(-tau/(par.dtau-eps)), (par.dtau>=0)*1e6 );
[Xstep,invXchol] = steplength(blk,X,dX,Xchol,invXchol);
timenew = clock;
ttime.pred_pstep = ttime.pred_pstep + etime(timenew,timeold); timeold=timenew;
Zstep = steplength(blk,Z,dZ,Zchol,invZchol);
pstep = min(1,gamused*min([Xstep,Zstep,kapstep,taustep]));
dstep = pstep;
kappred = kap + pstep*par.dkap;
taupred = tau + pstep*par.dtau;
trXZpred = trXZ + pstep*blktrace(blk,dX,Z) + dstep*blktrace(blk,X,dZ) ...
+ pstep*dstep*blktrace(blk,dX,dZ);
mupred = (trXZpred + kappred*taupred)/(nn+1);
mupredhist(iter) = mupred; %#ok
timenew = clock;
ttime.pred_dstep = ttime.pred_dstep + etime(timenew,timeold); timeold=timenew;
%%
%%-----------------------------------------
%% stopping criteria for predictor step.
%%-----------------------------------------
%%
if (min(pstep,dstep) < steptol) && (stoplevel)
msg = 'stop: steps in predictor too short';
if (printlevel)
fprintf('\n %s',msg);
fprintf(': pstep = %3.2e, dstep = %3.2e',pstep,dstep);
end
runhist.cputime(iter+1) = etime(clock,tstart);
termcode = -2;
breakyes = 1;
end
if (iter >= 2)
idx = max(2,iter-2) : iter;
pred_slow = all(mupredhist(idx)./mupredhist(idx-1) > 0.4);
idx = max(2,iter-5) : iter;
pred_convg_rate = mean(mupredhist(idx)./mupredhist(idx-1));
pred_slow = pred_slow + (mupred/mu > 5*pred_convg_rate);
end
if (~predcorr)
if (max(mu,infeas) < 1e-6) && (pred_slow) && (stoplevel)
msg = 'stop: lack of progress in predictor';
if (printlevel)
fprintf('\n %s',msg);
fprintf(': mupred/mu = %3.2f, pred_convg_rate = %3.2f.',...
mupred/mu,pred_convg_rate);
end
runhist.cputime(iter+1) = etime(clock,tstart);
termcode = -2;
breakyes = 1;
else
update_iter = 1;
end
end
%%
%%---------------------------------------------------------------
%% corrector step.
%%---------------------------------------------------------------
%%
if (predcorr) && (~breakyes)
step_pred = min(pstep,dstep);
if (mu > 1e-6)
if (step_pred < 1/sqrt(3));
expon_used = 1;
else
expon_used = max(expon,3*step_pred^2);
end
else
expon_used = max(1,min(expon,3*step_pred^2));
end
sigma = min( 1, (mupred/mu)^expon_used );
sigmu = sigma*mu;
%%
if (vers == 1)
[par,dX,dy,dZ] = HSDHKMcorr(blk,At,par,rp,Rd,sigmu,hRd,...
dX,dZ,coeff,L,X,Z);
elseif (vers == 2)
[par,dX,dy,dZ] = HSDNTcorr(blk,At,par,rp,Rd,sigmu,hRd,...
dX,dZ,coeff,L,X,Z);
end
if (solve_ok <= 0)
msg = 'stop: difficulty in computing corrector directions';
if (printlevel); fprintf('\n %s',msg); end
runhist.cputime(iter+1) = etime(clock,tstart);
termcode = -4;
break;
end
timenew = clock;
ttime.corr = ttime.corr + etime(timenew,timeold); timeold=timenew;
%%
%%-----------------------------------
%% step-lengths for corrector step
%%-----------------------------------
%%
if (gam == 0)
gamused = 0.9 + 0.09*min(pstep,dstep);
else
gamused = gam;
end
kapstep = max( (par.dkap<0)*(-kap/(par.dkap-eps)), (par.dkap>=0)*1e6 );
taustep = max( (par.dtau<0)*(-tau/(par.dtau-eps)), (par.dtau>=0)*1e6 );
Xstep = steplength(blk,X,dX,Xchol,invXchol);
timenew = clock;
ttime.corr_pstep = ttime.corr_pstep + etime(timenew,timeold); timeold=timenew;
Zstep = steplength(blk,Z,dZ,Zchol,invZchol);
timenew = clock;
pstep = min(1,gamused*min([Xstep,Zstep,kapstep,taustep]));
dstep = pstep;
kapcorr = kap + pstep*par.dkap;
taucorr = tau + pstep*par.dtau;
trXZcorr = trXZ + pstep*blktrace(blk,dX,Z) + dstep*blktrace(blk,X,dZ)...
+ pstep*dstep*blktrace(blk,dX,dZ);
mucorr = (trXZcorr+kapcorr*taucorr)/(nn+1);
ttime.corr_dstep = ttime.corr_dstep + etime(timenew,timeold); timeold=timenew;
%%
%%-----------------------------------------
%% stopping criteria for corrector step
%%-----------------------------------------
%%
if (iter >= 2)
idx = max(2,iter-2) : iter;
corr_slow = all(runhist.gap(idx)./runhist.gap(idx-1) > 0.8);
idx = max(2,iter-5) : iter;
corr_convg_rate = mean(runhist.gap(idx)./runhist.gap(idx-1));
corr_slow = corr_slow + (mucorr/mu > max(min(1,5*corr_convg_rate),0.8));
end
if (max(mu,infeas) < 1e-6) && (iter > 10) && (stoplevel) ...
&& (corr_slow && mucorr/mu > 1.0)
msg = 'stop: lack of progress in corrector';
if (printlevel)
fprintf('\n %s',msg);
fprintf(': mucorr/mu = %3.2f, corr_convg_rate = %3.2f',...
mucorr/mu,corr_convg_rate);
end
runhist.cputime(iter+1) = etime(clock,tstart);
termcode = -2;
breakyes = 1;
else
update_iter = 1;
end
end
%%
%%---------------------------------------------------------------
%% udpate iterate
%%---------------------------------------------------------------
%%
indef = [1 1];
if (update_iter)
for t = 1:5
[Xchol,indef(1)] = blkcholfun(blk,ops(X,'+',dX,pstep));
timenew = clock;
ttime.pchol = ttime.pchol + etime(timenew,timeold); timeold = timenew;
if (indef(1)); pstep = 0.8*pstep; else break; end
end
if (t > 1); pstep = gamused*pstep; end
for t = 1:5
[Zchol,indef(2)] = blkcholfun(blk,ops(Z,'+',dZ,dstep));
timenew = clock;
ttime.dchol = ttime.dchol + etime(timenew,timeold); timeold = timenew;
if (indef(2)); dstep = 0.8*dstep; else break; end
end
if (t > 1); dstep = gamused*dstep; end
AdX = AXfun(blk,At,par.permA,dX);
AXtmp = AX(1:m) + pstep*AdX(1:m); tautmp = par.tau+pstep*par.dtau;
prim_infeasnew = norm(b-AXtmp/tautmp)/normb;
pinfeas_bad(1) = (prim_infeasnew > max([1e-8,relgap,10*infeas]));
pinfeas_bad(2) = (prim_infeasnew > max([1e-4,20*prim_infeas]) ...
&& (infeas < 1e-2));
pinfeas_bad(3) = (max([relgap,dual_infeas]) < 1e-4) ...
&& (prim_infeasnew > max([2*prim_infeas,10*dual_infeas,1e-7]));
if any(indef)
msg = 'stop: X, Z not both positive definite';
if (printlevel); fprintf('\n %s',msg); end
termcode = -3;
breakyes = 1;
elseif any(pinfeas_bad)
if (stoplevel) && (max(pstep,dstep)<=1) && (kap < 1e-3) ...
&& (prim_infeasnew > dual_infeas);
msg = 'stop: primal infeas has deteriorated too much';
if (printlevel); fprintf('\n %s, %2.1e',msg,prim_infeasnew);
fprintf(' %2.1d,%2.1d,%2.1d',...
pinfeas_bad(1),pinfeas_bad(2),pinfeas_bad(3));
end
termcode = -7;
breakyes = 1;
end
end
if (~breakyes)
X = ops(X,'+',dX,pstep);
y = y + dstep*dy; Z = ops(Z,'+',dZ,dstep);
theta = max(0, theta + pstep*par.dtheta);
kap = kap + pstep*par.dkap;
if (tau + pstep*par.dtau > theta); tau = tau + pstep*par.dtau; end
end
end
%%
%%--------------------------------------------------
%% perturb Z: do this step before checking for break
%%--------------------------------------------------
perturb_Z = 1;
if (~breakyes) && (perturb_Z)
trXZtmp = blktrace(blk,X,Z);
trXE = blktrace(blk,X,EE);
Zpert = max(1e-12,0.2*min(relgap,prim_infeas)).*normC./normE;
Zpert = min(Zpert,0.1*trXZtmp./trXE);
Zpert = min([1,Zpert,1.5*Zpertold]);
if (infeas < 1e-2)
Z = ops(Z,'+',EE,Zpert);
[Zchol,indef(2)] = blkcholfun(blk,Z);
if any(indef(2))
msg = 'stop: Z not positive definite';
if (printlevel); fprintf('\n %s',msg); end
termcode = -3;
breakyes = 1;
end
end
Zpertold = Zpert;
end
%%
%%---------------------------------------------------------------
%% compute rp, Rd, infeasibities, etc.
%%---------------------------------------------------------------
%%
y2 = [y; tau; theta];
AX = AXfun(blk,At,par.permA,X);
rp = [zeros(m,1); kap; -abar] - AX - Bmat*y2;
% Rd = ops(Atyfun(blk,At,par.permA,par.isspAy,-y2),'-',Z);
trXZ = blktrace(blk,X,Z);
mu = (trXZ+kap*tau)/(nn+1);
obj = [blktrace(blk,C,X), b'*y]/tau;
gap = trXZ/tau^2;
relgap = gap/(1+mean(abs(obj)));
ZpATy = ops(Z,'+',Atyfun(blk,At,par.permA,par.isspAy,[y;0;0]));
ZpATynorm = ops(ZpATy,'norm');
prim_infeas = norm(b-AX(1:m)/tau)/normb;
dual_infeas = ops(ops(C,'-',ops(ZpATy,'/',tau)),'norm')/normC;
infeas = max(prim_infeas,dual_infeas);
runhist.pobj(iter+1) = obj(1);
runhist.dobj(iter+1) = obj(2);
runhist.gap(iter+1) = gap;
runhist.relgap(iter+1) = relgap;
runhist.pinfeas(iter+1) = prim_infeas;
runhist.dinfeas(iter+1) = dual_infeas;
runhist.infeas(iter+1) = infeas;
runhist.cputime(iter+1) = etime(clock,tstart);
runhist.step(iter+1) = min(pstep,dstep);
runhist.kappa(iter+1) = kap;
runhist.tau(iter+1) = tau;
runhist.theta(iter+1) = theta;
runhist.useLU(iter+1) = use_LU;
timenew = clock;
ttime.misc = ttime.misc + etime(timenew,timeold); % timeold = timenew;
[hh,mm,ss] = mytime(sum(runhist.cputime));
if (printlevel>=3)
fprintf('\n%2.0f|%4.3f|%4.3f|',iter,pstep,dstep);
fprintf('%2.1e|%2.1e|%2.1e|',prim_infeas,dual_infeas,gap);
fprintf('%- 7.6e| %s:%s:%s|',mean(obj),hh,mm,ss);
fprintf('%2.1e|%2.1e|%2.1e|',kap,tau,theta);
end
%%
%%--------------------------------------------------
%% check convergence.
%%--------------------------------------------------
param.termcode = termcode;
param.kap = kap;
param.tau = tau;
param.theta = theta;
param.iter = iter;
param.obj = obj;
param.gap = gap;
param.relgap = relgap;
param.mu = mu;
param.prim_infeas = prim_infeas;
param.dual_infeas = dual_infeas;
param.AX = AX(1:m)/tau;
param.ZpATynorm = ZpATynorm/tau;
param.normX = ops(X,'norm')/tau;
param.normZ = ops(Z,'norm')/tau;
if (~breakyes)
[param,breakyes,use_olditer,msg] = HSDsqlpcheckconvg(param,runhist);
termcode = param.termcode; %% important
if (use_olditer)
X = ops(X,'-',dX,pstep);
y = y - dstep*dy;
Z = ops(Z,'-',dZ,dstep);
kap = kap - pstep*par.dkap;
tau = tau - pstep*par.dtau;
theta = theta - pstep*par.dtheta;
prim_infeas = runhist.pinfeas(iter);
dual_infeas = runhist.dinfeas(iter);
gap = runhist.gap(iter); relgap = runhist.relgap(iter);
obj = [runhist.pobj(iter), runhist.dobj(iter)];
end
end
%%--------------------------------------------------
%% check for break
%%--------------------------------------------------
if ((prim_infeas < 1.5*prim_infeas_best) ...
|| (max(relgap,infeas) < 0.8*max(relgap_best,infeas_best))) ...
&& (max(relgap,dual_infeas) < 0.8*max(relgap_best,dual_infeas_best))
Xbest = X; ybest = y; Zbest = Z;
% kapbest = kap; taubest = tau; thetabest = theta;
prim_infeas_best = prim_infeas;
dual_infeas_best = dual_infeas;
relgap_best = relgap; infeas_best = infeas;
update_best(iter+1) = 1; %#ok
%%fprintf('#')
else
update_best(iter+1) = 0; %#ok
end
errbest = max(relgap_best,infeas_best);
if (errbest < 1e-4 && norm(update_best(max(1,iter-1):iter+1)) == 0)
msg = 'lack of progess in infeas';
if (printlevel); fprintf('\n %s',msg); end
termcode = -9;
breakyes = 1;
end
if (errbest < 1e-3 && max([relgap,infeas]) > 1.2*errbest && theta < 1e-10) ...
&& (kap < 1e-6)
msg = 'lack of progress in infeas';
if (printlevel); fprintf('\n %s',msg); end
termcode = -9;
breakyes = 1;
end
if (breakyes > 0.5); break; end
end
%%---------------------------------------------------------------
%% end of main loop
%%---------------------------------------------------------------
%%
use_bestiter = 1;
if (use_bestiter) && (param.termcode <= 0)
X = Xbest; y = ybest; Z = Zbest;
% kap = kapbest; tau = taubest; theta = thetabest;
trXZ = blktrace(blk,X,Z);
obj = [blktrace(blk,C,X), b'*y]/tau;
gap = trXZ/tau^2;
relgap = gap/(1+mean(abs(obj)));
AX = AXfun(blk,At,par.permA,X);
ZpATy = ops(Z,'+',Atyfun(blk,At,par.permA,par.isspAy,[y;0;0]));
ZpATynorm = ops(ZpATy,'norm');
prim_infeas = norm(b-AX(1:m)/tau)/normb;
dual_infeas = ops(ops(C,'-',ops(ZpATy,'/',tau)),'norm')/normC;
infeas = max(prim_infeas,dual_infeas);
runhist.pobj(iter+1) = obj(1);
runhist.dobj(iter+1) = obj(2);
runhist.gap(iter+1) = gap;
runhist.relgap(iter+1) = relgap;
runhist.pinfeas(iter+1) = prim_infeas;
runhist.dinfeas(iter+1) = dual_infeas;
runhist.infeas(iter+1) = infeas;
end
%%---------------------------------------------------------------
%% produce infeasibility certificates if appropriate
%%---------------------------------------------------------------
%%
X = ops(X,'/',tau); y = y/tau; Z = ops(Z,'/',tau);
if (iter >= 1)
param.termcode = termcode;
param.obj = obj;
param.relgap = relgap;
param.prim_infeas = prim_infeas;
param.dual_infeas = dual_infeas;
param.AX = AX(1:m)/tau;
param.ZpATynorm = ZpATynorm/tau;
[X,y,Z,resid,reldist,param,msg2] = ...
HSDsqlpmisc(blk,At,C,b,X,y,Z,par.permZ,param);
termcode = param.termcode;
end
%%
%%---------------------------------------------------------------
%% recover unrestricted blk from linear blk
%%---------------------------------------------------------------
%%
for p = 1:size(blk,1)
if (ublkidx(p) == 1)
n = blk{p,2}/2;
X{p} = X{p}(1:n)-X{p}(n+1:2*n);
Z{p} = Z{p}(1:n);
end
end
%%
%%---------------------------------------------------------------
%% print summary
%%---------------------------------------------------------------
%%
dimacs = [prim_infeas; 0; dual_infeas; 0];
dimacs = [dimacs; [-diff(obj); gap]/(1+sum(abs(obj)))];
info.dimacs = dimacs;
info.termcode = termcode;
info.iter = iter;
info.obj = obj;
info.gap = gap;
info.relgap = relgap;
info.pinfeas = prim_infeas;
info.dinfeas = dual_infeas;
info.cputime = sum(runhist.cputime);
info.time = ttime;
info.resid = resid;
info.reldist = reldist;
info.normX = ops(X,'norm');
info.normy = norm(y);
info.normZ = ops(Z,'norm');
info.normA = ops(At,'norm');
info.normb = norm(b);
info.normC = ops(C,'norm');
info.msg1 = msg;
info.msg2 = msg2;
%%
sqlpsummary(info,ttime,[],printlevel);
rand('state',randstate); %#ok
randn('state',randnstate); %#ok
%%*****************************************************************************

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