Page MenuHomec4science
Files F121189540

sqlpmain.m
No OneTemporary
Actions

File Metadata

Created
Wed, Jul 9, 05:25

sqlpmain.m
View Options

%%*************************************************************************
%% sqlp: main solver
%%
%%*************************************************************************
%% 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] = sqlpmain(blk,At,C,b,par,parbarrier,X0,y0,Z0)
global spdensity smallblkdim printlevel msg
global solve_ok use_LU exist_analytic_term numpertdiagschur
global schurfun schurfun_par
%%
% 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.
%%-----------------------------------------
%%
convertlen = 0;
[blk,At,C,X,Z,u2lblk,ublkidx] = sqlpu2lblk(blk,At,C,X,Z,par,convertlen);
for p = 1:size(blk,1)
% pblk = blk(p,:);
if (u2lblk(p) == 1)
n = 2*blk{p,2};
blk{p,1} = 'l'; blk{p,2} = n;
parbarrier{p} = zeros(1,n);
At{p} = [At{p}; -At{p}];
% tau = max(1,norm(C{p}));
C{p} = [C{p}; -C{p}];
msg = 'convert ublk to lblk';
if (printlevel); fprintf(' *** %s',msg); end
b2 = 1 + abs(b');
normCtmp = 1+norm(C{p});
normAtmp = 1+sqrt(sum(At{p}.*At{p}));
if (n > 1000)
const = sqrt(n);
else
const = n;
end
if (par.startpoint == 1)
X{p} = const* max([1,b2./normAtmp]) *ones(n,1);
Z{p} = const* max([1,normAtmp/sqrt(n),normCtmp/sqrt(n)]) *ones(n,1);
X{p} = X{p}.*(1+1e-10*randmat(n,1,0,'u'));
Z{p} = Z{p}.*(1+1e-10*randmat(n,1,0,'u'));
else
const = max(abs(X{p})) + 100;
X{p} = [X{p}+const; const*ones(n/2,1)];
%%old: const = 100; Z{p} = [const*ones(n/2,1); const*ones(n/2,1)];
Z{p} = [abs(Z0{p}); abs(Z0{p})] + 1e-4;
end
end
end
%%-----------------------------------------
%% check whether {A1,...,Am} is
%% linearly independent.
%%-----------------------------------------
%%
m0 = length(b);
[At,b,y,indeprows,par.depconstr,feasible,par.AAt] = ...
checkdepconstr(blk,At,b,y,rmdepconstr);
if (~feasible)
obj = []; X = cell(size(blk,1),1); y = []; Z = cell(size(blk,1),1);
runhist = [];
msg = 'SQLP is not feasible';
if (printlevel); fprintf('\n %s \n',msg); end
return;
end
par.normAAt = norm(par.AAt,'fro');
%%
%%-----------------------------------------
%% scale SQLP data. Note: must be done only
%% after checkdepconstr
%%-----------------------------------------
%%
normA2 = 1+ops(At,'norm');
normb2 = 1+norm(b);
normC2 = 1+ops(C,'norm');
normX0 = 1+ops(X0,'norm');
normZ0 = 1+ops(Z0,'norm');
if (scale_data)
[At,C,b,normA,normC,normb,X,y,Z] = scaling(blk,At,C,b,X,y,Z);
else
normA = 1; normC = 1; normb = 1;
end
%%
%%-----------------------------------------
%% find the combined list of non-zero
%% elements of Aj, j = 1:k, for each k.
%% IMPORTANT NOTE: Ak, C are permuted.
%%-----------------------------------------
%%
par.numcolAt = length(b);
[At,C,X,Z,par.permA,par.permZ] = sortA(blk,At,C,b,X,Z);
[par.isspA,par.nzlistA,par.nzlistAsum,par.isspAy,par.nzlistAy] = nzlist(blk,At,par);
%%
%%-----------------------------------------
%% create an artifical non-negative block
%% for a purely log-barrier problem
%%-----------------------------------------
%%
numblkold = size(blk,1);
nn = 0;
for p = 1:size(blk,1);
pblk = blk(p,:);
idx = find(parbarrier{p}==0);
if ~isempty(idx);
if strcmp(pblk{1},'l')
nn = nn + length(idx);
elseif strcmp(pblk{1},'q')
nn = nn + sum(pblk{2}(idx));
elseif strcmp(pblk{1},'s')
nn = nn + sum(pblk{2}(idx));
end
end
end
if (nn==0)
analytic_prob = 1;
numblk = size(blk,1)+1;
blk{numblk,1} = 'l'; blk{numblk,2} = 1;
At{numblk,1} = sparse(1,length(b));
C{numblk,1} = 1;
X{numblk,1} = 1e3;
Z{numblk,1} = 1e3;
parbarrier{numblk,1} = 0;
u2lblk(numblk,1) = 0;
nn = nn + 1;
else
analytic_prob = 0;
end
%%
exist_analytic_term = 0;
for p = 1:size(blk,1);
if any(parbarrier{p} > 0),
exist_analytic_term = 1;
end
end
%%-----------------------------------------
%% initialization
%%-----------------------------------------
%%
EE = ops(blk,'identity');
normE2 = ops(EE,'norm'); Zpertold = 1;
for p = 1:size(blk,1)
% normCC(p) = 1+ops(C(p),'norm');
normEE(p) = 1+ops(EE(p),'norm'); %#ok
end
[Xchol,indef(1)] = blkcholfun(blk,X);
[Zchol,indef(2)] = blkcholfun(blk,Z);
if any(indef)
msg = 'stop: X or Z not positive definite';
if (printlevel); fprintf('\n %s\n',msg); end
info.termcode = -3;
info.msg1 = msg;
obj = []; X = cell(size(blk,1),1); y = []; Z = cell(size(blk,1),1);
runhist = [];
return;
end
AX = AXfun(blk,At,par.permA,X);
rp = b-AX;
ZpATy = ops(Z,'+',Atyfun(blk,At,par.permA,par.isspAy,y));
ZpATynorm = ops(ZpATy,'norm');
Rd = ops(C,'-',ZpATy);
objadd0 = 0;
if (scale_data)
for p = 1:size(blk,1)
pblk = blk(p,:);
objadd0 = objadd0 + sum(parbarrier{p}.*pblk{2})*log(normA{p});
end
end
objadd = blkbarrier(blk,X,Z,Xchol,Zchol,parbarrier) + objadd0;
obj = (normb*normC)*[blktrace(blk,C,X), b'*y] + objadd;
gap = (normb*normC)*blktrace(blk,X,Z) - diff(objadd);
relgap = gap/(1+sum(abs(obj)));
prim_infeas = norm(rp)/normb2;
dual_infeas = ops(Rd,'norm')/normC2;
infeas = max(prim_infeas,dual_infeas);
if (scale_data)
infeas_org(1) = prim_infeas*normb;
infeas_org(2) = dual_infeas*normC;
else
infeas_org = [0,0];
end
trXZ = blktrace(blk,X,Z,parbarrier);
if (nn > 0); mu = trXZ/nn; else mu = gap/ops(X,'getM'); end
normX = ops(X,'norm');
%%
termcode = 0; restart = 0;
pstep = 1; dstep = 1; pred_convg_rate = 1; corr_convg_rate = 1;
% prim_infeas_min = prim_infeas;
% dual_infeas_min = dual_infeas;
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 = []; msg3 = [];
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.pstep = 0;
runhist.dstep = 0;
runhist.step = 0;
runhist.normX = normX;
runhist.cputime = etime(clock,tstart);
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: Infeasible path-following algorithms');
fprintf('\n********************************************');
fprintf('***********************\n');
[hh,mm,ss] = mytime(ttime.preproc);
if (printlevel>=3)
fprintf(' version predcorr gam expon scale_data\n');
if (vers == 1); fprintf(' HKM '); elseif (vers == 2); fprintf(' NT '); end
fprintf(' %1.0f %4.3f',predcorr,gam);
fprintf(' %1.0f %1.0f %1.0f\n',expon,scale_data);
fprintf('\nit pstep dstep pinfeas dinfeas gap')
fprintf(' prim-obj dual-obj cputime\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 %- 7.6e| %s:%s:%s|',gap,obj(1),obj(2),hh,mm,ss);
end
end
%%
%%---------------------------------------------------------------
%% start main loop
%%---------------------------------------------------------------
%%
param.termcode = termcode;
param.iter = 0;
param.obj = obj;
param.relgap = relgap;
param.prim_infeas = prim_infeas; param.dual_infeas = dual_infeas;
param.homRd = homRd; param.homrp = homrp;
param.AX = AX; param.ZpATynorm = ZpATynorm;
param.normA = normA;
param.normb = normb; param.normC = normC;
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.scale_data = scale_data;
param.printlevel = printlevel;
param.ublksize = ublksize;
Xbest = X; ybest = y; Zbest = Z;
%%
for iter = 1:maxit;
tstart = clock;
timeold = tstart;
update_iter = 0; breakyes = 0;
pred_slow = 0; corr_slow = 0; % step_short = 0;
par.parbarrier = parbarrier;
par.iter = iter;
par.obj = obj;
par.relgap = relgap;
par.pinfeas = prim_infeas;
par.dinfeas = dual_infeas;
par.rp = rp;
par.y = y;
par.dy = dy;
par.normX = normX;
par.ZpATynorm = ZpATynorm;
%%if (printlevel > 2); fprintf(' %2.1e',par.normX); end
if (iter == 1 || restart); Cpert = min(1,normC2/ops(EE,'norm')); end
if (runhist.dinfeas(1) > 1e-3) && (~exist_analytic_term) ...
&& (relgap > 1e-4)
if (par.normX > 5e3 && iter < 20)
Cpert = Cpert*0.5;
elseif (par.normX > 5e2 && iter < 20);
Cpert = Cpert*0.3;
else
Cpert = Cpert*0.1;
end
Rd = ops(Rd,'+',EE,Cpert);
%%if (printlevel > 2); fprintf('|%2.1e',Cpert); end
end
%%---------------------------------------------------------------
%% predictor step.
%%---------------------------------------------------------------
%%
if (predcorr)
sigma = 0;
else
sigma = 1-0.9*min(pstep,dstep);
if (iter == 1); sigma = 0.5; end;
end
sigmu = cell(size(blk,1),1);
for p = 1:size(blk,1)
sigmu{p} = max(sigma*mu, parbarrier{p}');
end
invXchol = cell(size(blk,1),1);
invZchol = ops(Zchol,'inv');
if (vers == 1);
[par,dX,dy,dZ,coeff,L,hRd] = ...
HKMpred(blk,At,par,rp,Rd,sigmu,X,Z,invZchol);
elseif (vers == 2);
[par,dX,dy,dZ,coeff,L,hRd] = ...
NTpred(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.pinfeas(iter+1) = runhist.pinfeas(iter);
runhist.dinfeas(iter+1) = runhist.dinfeas(iter);
runhist.relgap(iter+1) = runhist.relgap(iter);
runhist.cputime(iter+1) = etime(clock,tstart);
termcode = -4;
break; %% do not ues breakyes = 1
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
[Xstep,invXchol] = steplength(blk,X,dX,Xchol,invXchol);
pstep = min(1,gamused*full(Xstep));
timenew = clock;
ttime.pred_pstep = ttime.pred_pstep + etime(timenew,timeold); timeold = timenew;
Zstep = steplength(blk,Z,dZ,Zchol,invZchol);
dstep = min(1,gamused*full(Zstep));
trXZnew = trXZ + pstep*blktrace(blk,dX,Z,parbarrier) ...
+ dstep*blktrace(blk,X,dZ,parbarrier) ...
+ pstep*dstep*blktrace(blk,dX,dZ,parbarrier);
if (nn > 0); mupred = trXZnew/nn; else mupred = 1e-16; end
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) && (iter > 10)
msg = 'stop: steps in predictor too short';
if (printlevel)
fprintf('\n %s',msg);
fprintf(': pstep = %3.2e, dstep = %3.2e\n',pstep,dstep);
end
runhist.cputime(iter+1) = etime(clock,tstart);
termcode = -2;
breakyes = 1;
end
if (~predcorr)
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 (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
if (nn==0)
sigma = 0.2;
elseif (mupred < 0)
sigma = 0.8;
else
sigma = min(1, (mupred/mu)^expon_used);
end
sigmu = cell(size(blk,1),1);
for p = 1:size(blk,1)
sigmu{p} = max(sigma*mu, parbarrier{p}');
end
if (vers == 1)
[dX,dy,dZ] = HKMcorr(blk,At,par,rp,Rd,sigmu,hRd,...
dX,dZ,coeff,L,X,Z);
elseif (vers == 2)
[dX,dy,dZ] = NTcorr(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.pinfeas(iter+1) = runhist.pinfeas(iter);
runhist.dinfeas(iter+1) = runhist.dinfeas(iter);
runhist.relgap(iter+1) = runhist.relgap(iter);
runhist.cputime(iter+1) = etime(clock,tstart);
termcode = -4;
break; %% do not ues breakyes = 1
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
Xstep = steplength(blk,X,dX,Xchol,invXchol);
pstep = min(1,gamused*full(Xstep));
timenew = clock;
ttime.corr_pstep = ttime.corr_pstep+etime(timenew,timeold); timeold = timenew;
Zstep = steplength(blk,Z,dZ,Zchol,invZchol);
dstep = min(1,gamused*full(Zstep));
trXZnew = trXZ + pstep*blktrace(blk,dX,Z,parbarrier) ...
+ dstep*blktrace(blk,X,dZ,parbarrier)...
+ pstep*dstep*blktrace(blk,dX,dZ,parbarrier);
if (nn > 0); mucorr = trXZnew/nn; else mucorr = 1e-16; end
timenew = clock;
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(relgap,infeas) < 1e-6) && (iter > 20) ...
&& (corr_slow > 1) && (stoplevel)
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
%%-------------------------------------------
AXtmp = AX + pstep*AXfun(blk,At,par.permA,dX);
prim_infeasnew = norm(b-AXtmp)/normb2;
if (relgap < 5*infeas); alpha = 1e2; else alpha = 1e3; end
if any(indef)
if indef(1); msg = 'stop: X not positive definite'; end
if indef(2); msg = 'stop: Z not positive definite'; end
if (printlevel); fprintf('\n %s',msg); end
termcode = -3;
breakyes = 1;
elseif (prim_infeasnew > max([1e-8,relgap,20*prim_infeas]) && iter > 10) ...
|| (prim_infeasnew > max([1e-7,1e3*prim_infeas,0.1*relgap]) && relgap < 1e-2) ...
|| (prim_infeasnew > alpha*max([1e-9,param.prim_infeas_min]) ...
&& (prim_infeasnew > max([3*prim_infeas,0.1*relgap])) ...
&& (iter > 25) && (dual_infeas < 1e-6) && (relgap < 0.1)) ...
|| ((prim_infeasnew > 1e3*prim_infeas && prim_infeasnew > 1e-12) ...
&& (max(relgap,dual_infeas) < 1e-8))
if (stoplevel)
msg = 'stop: primal infeas has deteriorated too much';
if (printlevel); fprintf('\n %s, %2.1e',msg,prim_infeasnew); end
termcode = -7;
breakyes = 1;
end
elseif (trXZnew > 1.05*runhist.gap(iter)) && (~exist_analytic_term) ...
&& ((infeas < 1e-5) && (relgap < 1e-4) && (iter > 20) ...
|| (max(infeas,relgap) < 1e-7) && (iter > 10))
if (stoplevel)
msg = 'stop: progress in duality gap has deteriorated';
if (printlevel); fprintf('\n %s, %2.1e',msg,trXZnew); end
termcode = -8;
breakyes = 1;
end
else
X = ops(X,'+',dX,pstep);
y = y + dstep*dy;
Z = ops(Z,'+',dZ,dstep);
end
end
%%---------------------------------------------------------------
%% adjust linear blk arising from unrestricted blk
%%---------------------------------------------------------------
if (~breakyes)
for p = 1:size(blk,1)
if (u2lblk(p) == 1)
len = blk{p,2}/2;
xtmp = min(X{p}(1:len),X{p}(len+1:2*len));
alpha = 0.8;
X{p}(1:len) = X{p}(1:len) - alpha*xtmp;
X{p}(len+1:2*len) = X{p}(len+1:2*len) - alpha*xtmp;
if (mu < 1e-4) %% old: (mu < 1e-7)
Z{p} = 0.5*mu./max(1,X{p}); %% good to keep this step
else
ztmp = min(1,max(Z{p}(1:len),Z{p}(len+1:2*len)));
if (dual_infeas > 1e-4 && dstep < 0.2)
beta = 0.3;
else
beta = 0.0;
end
%% important to set beta = 0 at later stage.
Z{p}(1:len) = Z{p}(1:len) + beta*ztmp;
Z{p}(len+1:2*len) = Z{p}(len+1:2*len) + beta*ztmp;
end
end
end
end
%%--------------------------------------------------
%% perturb Z: do this step before checking for break
%%--------------------------------------------------
if (~breakyes) && (~exist_analytic_term)
trXZtmp = blktrace(blk,X,Z);
trXE = blktrace(blk,X,EE);
Zpert = max(1e-12,0.2*min(relgap,prim_infeas)).*normC2./normE2;
Zpert = min(Zpert,0.1*trXZtmp./trXE);
Zpert = min([1,Zpert,1.5*Zpertold]);
if (infeas < 0.1)
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
%%if (printlevel > 2); fprintf(' %2.1e',Zpert); end
end
Zpertold = Zpert;
end
%%---------------------------------------------------------------
%% compute rp, Rd, infeasibities, etc
%%---------------------------------------------------------------
%%
AX = AXfun(blk,At,par.permA,X);
rp = b-AX;
ZpATy = ops(Z,'+',Atyfun(blk,At,par.permA,par.isspAy,y));
ZpATynorm = ops(ZpATy,'norm');
Rd = ops(C,'-',ZpATy);
objadd = blkbarrier(blk,X,Z,Xchol,Zchol,parbarrier) + objadd0;
obj = (normb*normC)*[blktrace(blk,C,X), b'*y] + objadd;
gap = (normb*normC)*blktrace(blk,X,Z) - diff(objadd);
relgap = gap/(1+sum(abs(obj)));
prim_infeas = norm(rp)/normb2;
dual_infeas = ops(Rd,'norm')/normC2;
infeas = max(prim_infeas,dual_infeas);
if (scale_data)
infeas_org(1) = prim_infeas*normb;
infeas_org(2) = dual_infeas*normC;
end
homRd = inf; homrp = inf;
if (ops(parbarrier,'norm') == 0)
if (obj(2) > 0); homRd = ZpATynorm/(obj(2)); end
if (obj(1) < 0); homrp = norm(AX)/(-obj(1))/(normC); end
end
trXZ = blktrace(blk,X,Z,parbarrier);
if (nn > 0); mu = trXZ/nn; else mu = gap/ops(X,'getM'); end
normX = ops(X,'norm');
%%
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.pstep(iter+1) = pstep;
runhist.dstep(iter+1) = dstep;
runhist.step(iter+1) = min(pstep,dstep);
runhist.normX(iter+1) = normX;
runhist.cputime(iter+1) = etime(clock,tstart);
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 %- 7.6e| %s:%s:%s|',obj(1),obj(2),hh,mm,ss);
end
%%--------------------------------------------------
%% check convergence
%%--------------------------------------------------
param.use_LU = use_LU;
param.stoplevel = stoplevel;
param.termcode = termcode;
param.iter = iter;
param.obj = obj;
param.gap = gap;
param.relgap = relgap;
param.prim_infeas = prim_infeas;
param.dual_infeas = dual_infeas;
param.mu = mu;
param.homRd = homRd;
param.homrp = homrp;
param.AX = AX;
param.ZpATynorm = ZpATynorm;
param.normX = ops(X,'norm');
param.normZ = ops(Z,'norm');
param.numpertdiagschur = numpertdiagschur;
if (~breakyes)
[param,breakyes,restart,msg2] = sqlpcheckconvg(param,runhist);
end
if (restart)
[X,y,Z] = infeaspt(blk,At,C,b,2,1e5);
rp = b-AXfun(blk,At,par.permA,X);
ZpATy = ops(Z,'+',Atyfun(blk,At,par.permA,par.isspAy,y));
Rd = ops(C,'-',ZpATy);
trXZ = blktrace(blk,X,Z,parbarrier);
mu = trXZ/nn;
gap = (normb*normC)*blktrace(blk,X,Z) - diff(objadd);
prim_infeas = norm(rp)/normb2;
dual_infeas = ops(Rd,'norm')/normC2;
infeas = max(prim_infeas,dual_infeas);
[Xchol,indef(1)] = blkcholfun(blk,X);
[Zchol,indef(2)] = blkcholfun(blk,Z); %#ok
stoplevel = 3;
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;
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
if (max(relgap_best,infeas_best) < 1e-4 ...
&& norm(update_best(max(1,iter-1):iter+1)) == 0)
msg = 'lack of progress in infeas';
if (printlevel); fprintf('\n %s',msg); end
termcode = -9;
breakyes = 1;
end
if (breakyes); break; end
end
%%---------------------------------------------------------------
%% end of main loop
%%---------------------------------------------------------------
%%
use_bestiter = 1;
if (use_bestiter) && (param.termcode <= 0)
X = Xbest; y = ybest; Z = Zbest;
Xchol = blkcholfun(blk,X);
Zchol = blkcholfun(blk,Z);
AX = AXfun(blk,At,par.permA,X);
rp = b-AX;
ZpATy = ops(Z,'+',Atyfun(blk,At,par.permA,par.isspAy,y));
Rd = ops(C,'-',ZpATy);
objadd = blkbarrier(blk,X,Z,Xchol,Zchol,parbarrier) + objadd0;
obj = (normb*normC)*[blktrace(blk,C,X), b'*y] + objadd;
gap = (normb*normC)*blktrace(blk,X,Z) - diff(objadd);
relgap = gap/(1+sum(abs(obj)));
prim_infeas = norm(rp)/normb2;
dual_infeas = ops(Rd,'norm')/normC2;
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
%%---------------------------------------------------------------
%% unscale and produce infeasibility certificates if appropriate
%%---------------------------------------------------------------
if (iter >= 1)
[X,y,Z,termcode,resid,reldist,msg3] = ...
sqlpmisc(blk,At,C,b,X,y,Z,par.permZ,param);
end
%%---------------------------------------------------------------
%% recover unrestricted blk from linear blk
%%---------------------------------------------------------------
%%
for p = 1:size(blk,1)
if (u2lblk(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
for p = 1:size(ublkidx,1)
if ~isempty(ublkidx{p,2})
n0 = ublkidx{p,1}; idxB = setdiff((1:n0)',ublkidx{p,2});
tmp = zeros(n0,1); tmp(idxB) = X{p}; X{p} = tmp;
tmp = zeros(n0,1); tmp(idxB) = Z{p}; Z{p} = tmp;
end
end
if (analytic_prob)
X = X(1:numblkold); Z = Z(1:numblkold);
end
%%---------------------------------------------------------------
%% print summary
%%---------------------------------------------------------------
%%
maxC = 1+ops(ops(C,'abs'),'max');
maxb = 1+max(abs(b));
if (scale_data)
dimacs = [infeas_org(1)*normb2/maxb; 0; infeas_org(2)*normC2/maxC; 0];
else
dimacs = [prim_infeas*normb2/maxb; 0; dual_infeas*normC2/maxC; 0];
end
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.normb = normb2; info.maxb = maxb;
info.normC = normC2; info.maxC = maxC;
info.normA = normA2;
info.msg1 = msg;
info.msg2 = msg2;
info.msg3 = msg3;
sqlpsummary(info,ttime,infeas_org,printlevel);
%%*****************************************************************************

Event Timeline

c4science · Help