Lagrangian Multipliers (for Matrix constraints) update
0001 % Lagrangian Multipliers (for Matrix constraints) update 0002 function [] = lmltm_update(obj) 0003 0004 % obviously only pen/bar 0005 % I have in the object: UYbox, UYboxnew, UA, UAnew - cell array with indices 0006 % matching Yboxindphi & Aindphi 0007 0008 mu2 = obj.allopts.mmlt_update; 0009 0010 % compute new candidates in *new; this will be done in eval*() as a by-product 0011 0012 % matrix variable - pen/bar 0013 for k=obj.Yboxindphi 0014 pkx=obj.PYbox(k); %2*p(sdpdata.Ng+k); 0015 %Akx=evalax(x,k,sdpdata); 0016 % mapping xall first !!! TODO take obj.Y{...} 0017 Ykx = obj.Y{obj.Yboxmap(k)}; 0018 Akx=obj.Yboxshift(k)*speye(size(Ykx)) + obj.Yboxmlt(k)*Ykx; 0019 umatk=obj.UYbox{k}; 0020 0021 %Z=(pkx*speye(size(Akx))-Akx); 0022 Z=(pkx*speye(size(Akx))-Akx); 0023 invZ=inv(Z); 0024 pZUZ=pkx^2*invZ*umatk*invZ; 0025 obj.UYboxnew{k}=pZUZ; 0026 end 0027 0028 % matrix constraints - pen/bar 0029 for k=obj.Aindphi 0030 pkx=obj.PA(k); % I used to use 2* !!!!!!!! 0031 % TODO need to map the matrix first! - is it correct??? 0032 kuser=obj.Amap(k); 0033 [Akuserx, obj.userdata] = obj.mconfun(obj.x, obj.Y, kuser, obj.userdata); 0034 Akx = obj.Ashift(k)*speye(size(Akuserx)) + obj.Amlt(k) .* Akuserx; 0035 umatk=obj.UA{k}; 0036 0037 %Z=(pkx*speye(size(Akx))-Akx); 0038 Z=(pkx*speye(size(Akx))-Akx); 0039 invZ=inv(Z); 0040 pZUZ=pkx^2*invZ*umatk*invZ; 0041 obj.UAnew{k}=pZUZ; 0042 end 0043 0044 % update as in update_multipliers() @ pbmfnc/Pennon1.0 0045 % [in SDP/BMI there is still active one more option] 0046 % rStabilize = 1.0E-16*sqrt((double)(Umat->mat[i]->m)*diagnorm(Umat->mat[i], nSparse)); 0047 % m_stabilize(Umat->mat[i], rStabilize, nSparse); 0048 % rLambda = 1-mu2; 0049 % m_ConvComb(rLambda, Umattmp->mat[i], Umat->mat[i], Umat->mat[i], nSparse); 0050 % rStabilize = 1.0E-16*sqrt((double)(Umat->mat[i]->m)*diagnorm(Umat->mat[i], nSparse)); 0051 % m_stabilize(Umat->mat[i], rStabilize, nSparse); 0052 % Note that in the code Umat & Umattmp are swapped (Umat is the new one in 0053 % this part) 0054 0055 % matrix variable - pen/bar 0056 for k=obj.Yboxindphi 0057 umatk = obj.UYboxnew{k}; 0058 umatk = m_stabilize(umatk); 0059 %lambda=1-mu2; 0060 %umatk = (1-lambda)*old + lambda*new; 0061 umatk = mu2*obj.UYbox{k} + (1-mu2)*umatk; 0062 obj.UYbox{k} = m_stabilize(umatk); 0063 % & push it back but keep the 'old ones'?? 0064 % are they used behind update_multipliers?? 0065 end 0066 0067 % matrix constraints - pen/bar 0068 for k=obj.Aindphi 0069 umatk = obj.UAnew{k}; 0070 umatk = m_stabilize(umatk); 0071 %lambda=1-mu2; 0072 %umatk = (1-lambda)*old + lambda*new; 0073 umatk = mu2*obj.UA{k} + (1-mu2)*umatk; 0074 obj.UA{k} = m_stabilize(umatk); 0075 % & push it back but keep the 'old ones'?? 0076 % are they used behind update_multipliers?? 0077 end 0078 0079 end 0080 0081 %%%%%%%%%%%%%%%%%%%%%%%%%%%%% 0082 % stabilize M 0083 % only on diag elements: m_ii = |m_ii| + r 0084 % where r is given by the norm of the diag 0085 % how to access the diagonal of a dense matrix? 0086 % M(1:n+1:end) = newdiag 0087 % iii=1:n+1:n^2; M(iii)=... [slightly slower] 0088 % or normal for loop 0089 function [M] = m_stabilize(M) 0090 [n m] = size(M); 0091 Mdiag = diag(M); 0092 rStabilize = 1.0e-16*realsqrt(n*norm(Mdiag,2)); 0093 M(1:n+1:end) = abs(Mdiag) + rStabilize; 0094 end 0095 0096