%%***************************************************************************** %% 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 = [ ]. %% (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 . %% 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 4.0 %% Copyright (c) 1997 by %% Kim-Chuan Toh, Michael J. Todd, Reha 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'); rand('state',0); randn('state',0); %% 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); [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) && (theta > 1e-10) %%2nd condition added: 2017-Jun-13 [At,Cpert] = HSDsqlpCpert(blk,At,par,C,X,Cpert,runhist); maxCpert(iter) = max(Cpert); %%fprintf(' %2.1e',max(Cpert)); if (iter > 10 & norm(diff(maxCpert([iter-3,iter]))) < 1e-13) Cpert = 0.5*Cpert; maxCpert(iter) = max(Cpert); 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; 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 %%-------------------------------------------------- if (theta > 1e-10) %%added: 2017-Jun-13 perturb_Z = 1; else perturb_Z = 0; %% do not perturb when theta is small end 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*0.1,infeas) < 0.8*max(relgap_best,infeas_best))) ... & (max(relgap*0.1,dual_infeas) < 0.8*max(relgap_best,dual_infeas_best)) %% ()*1 -> ()*0.1: 2017-Jun-13 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; %%fprintf('#') else update_best(iter+1) = 0; 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: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); randn('state',randnstate); %%*****************************************************************************