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Copy pathMGPAD_differentFt_cellF.m
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MGPAD_differentFt_cellF.m
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function [ Z,Y,details] = MGPAD_differentFt_cellF(sys,Ptree,Tree,V,ops)
%This function is implements the GPAD algorithm to solve an optimization
%problem. The inputs the system are the system dynamics, the tree
%structure, all the off-line elements that are calculated earlier that are
%to be used by the GPAD. additional options about the inital fesible dual
%variable.
%The terminal constraints are different.
% In this algorithm the dual variables correspond to nodes of the tree.
%monotonicity on primal with theta restart to [1 1]
Ns=length(Tree.leaves);% total scenarios in the tree
Nd=length(Tree.stage);%toal nodes in the tree
% Initalizing the dual varibables
Y.y0=zeros(Nd-Ns,size(sys.F{1},1));
Y.y1=zeros(Nd-Ns,size(sys.F{1},1));
prm_fes_term=cell(Ns,1);
epsilon_prm=1;
for i=1:Ns
Y.yt0{i,:}=zeros(1,size(sys.Ft{i,1},1));
Y.yt1{i,:}=zeros(1,size(sys.Ft{i,1},1));
prm_fes_term{i,1}=zeros(size(sys.Ft{i,1},1),1);
end
prm_fes=zeros(size(sys.F{1},1),Nd-Ns);
g_nodes=zeros(size(sys.F{1},1),Nd-Ns);
for i=1:Nd-Ns
g_nodes(:,i)=sys.g{i,1};
end
g_nodes_term=sys.gt;
theta=[1 1]';
tic
j=1;
W_minyt=zeros(Ns,1);
details.restart=0;
details.term_crit=zeros(1,4);
while(j<ops.steps)
% Step 1: accelerated step
W.y=Y.y1+theta(2)*(1/theta(1)-1)*(Y.y1-Y.y0);
for i=1:Ns
W.yt{i,1}=Y.yt1{i,1}+theta(2)*(1/theta(1)-1)*(Y.yt1{i,1}-Y.yt0{i,1});
W_minyt(i,1)=min(W.yt{i,1});
end
%step 2: argmin of the lagrangian using dynamic programming
Z=GPAD_dynamic_calculation_Ft(sys,Ptree,Tree,W,ops.x0);
%check for restart crieteria
iter=j;
details.prm_cst(iter)=0;%primal cost;
for i=1:Nd-Ns
details.prm_cst(iter)=details.prm_cst(iter)+Tree.prob(i,1)*(Z.X(:,i)'*V.Q*Z.X(:,i)+Z.U(:,i)'*V.R*Z.U(:,i));
end
for i=1:Ns
details.prm_cst(iter)=details.prm_cst(iter)+Tree.prob(Tree.leaves(i))*(Z.X(:,Tree.leaves(i))'*V.Vf{i,1}*...
Z.X(:,Tree.leaves(i)));
end
if(j>1)
if(mod(details.restart,2)==0)
if(details.prm_cst(iter-1)>details.prm_cst(iter))
details.restart=details.restart+1;
details.restart_iter(details.restart)=iter;
theta=[1 1]';
W.y=Y.y1+theta(2)*(1/theta(1)-1)*(Y.y1-Y.y0);
%Wt.y=Y.y1;
for i=1:Ns
W.yt{i,1}=Y.yt1{i,1}+theta(2)*(1/theta(1)-1)*(Y.yt1{i,1}-Y.yt0{i,1});
W_minyt(i,1)=min(W.yt{i,1});
%Wt.yt{i,1}=Y.yt1{i,1};
end
Z=GPAD_dynamic_calculation_Ft(sys,Ptree,Tree,W,ops.x0);
details.prm_cst(iter)=0;
for i=1:Nd-Ns
details.prm_cst(iter)=details.prm_cst(iter)+Tree.prob(i,1)*(Z.X(:,i)'*V.Q*Z.X(:,i)+Z.U(:,i)'*V.R*Z.U(:,i));
end
for i=1:Ns
details.prm_cst(iter)=details.prm_cst(iter)+Tree.prob(Tree.leaves(i))*(Z.X(:,Tree.leaves(i))'*V.Vf{i,1}*...
Z.X(:,Tree.leaves(i)));
end
end
else
if(details.prm_cst(iter-1)<details.prm_cst(iter))
details.restart=details.restart+1;
details.restart_iter(details.restart)=iter;
theta=[1 1]';
W.y=Y.y1+theta(2)*(1/theta(1)-1)*(Y.y1-Y.y0);
%Wt.y=Y.y1;
for i=1:Ns
W.yt{i,1}=Y.yt1{i,1}+theta(2)*(1/theta(1)-1)*(Y.yt1{i,1}-Y.yt0{i,1});
W_minyt(i,1)=min(W.yt{i,1});
%Wt.yt{i,1}=Y.yt1{i,1};
end
Z=GPAD_dynamic_calculation_Ft(sys,Ptree,Tree,W,ops.x0);
details.prm_cst(iter)=0;
for i=1:Nd-Ns
details.prm_cst(iter)=details.prm_cst(iter)+Tree.prob(i,1)*(Z.X(:,i)'*V.Q*Z.X(:,i)+Z.U(:,i)'*V.R*Z.U(:,i));
end
for i=1:Ns
details.prm_cst(iter)=details.prm_cst(iter)+Tree.prob(Tree.leaves(i))*(Z.X(:,Tree.leaves(i))'*V.Vf{i,1}*...
Z.X(:,Tree.leaves(i)));
end
end
end
if(details.prm_cst(iter-1)>details.prm_cst(iter))
end
end
%step 3: Projection of y on the positive quadrant.
Y.y0=Y.y1;
Y.yt0=Y.yt1;
for i=1:Tree.ancestor(Tree.leaves(end))
prm_fes(:,i)=sys.F{i}*Z.X(:,i)+sys.G{i}*Z.U(:,i);
Y.y1(i,:)=(max(0,W.y(i,:)'+ops.alpha*(prm_fes(:,i)-g_nodes(:,i))))';
end
for i=1:length(Tree.leaves)
prm_fes_term{i,1}=sys.Ft{i,1}*Z.X(:,Tree.leaves(i));
Y.yt1{i,1}=max(0,W.yt{i,:}+ops.alpha*(prm_fes_term{i,1}-sys.gt{i,1})');
end
%termination criteria
if(j==1)
prm_avg_next=prm_fes;
prm_avg_term_next=prm_fes_term;
epsilon_prm_avg=max( max(max(prm_fes-g_nodes)), ...
max(max(cell2mat(prm_fes_term)-cell2mat(g_nodes_term))) );
else
prm_avg_next=(1-theta(2))*prm_avg_next+theta(2)*prm_fes;
for m=1:Ns
prm_avg_term_next{m,1}=(1-theta(2))*prm_avg_term_next{m,1}+theta(2)*prm_fes_term{m,1};
end
epsilon_prm_avg=max(max(max(prm_avg_next-g_nodes)),...
max(max(cell2mat(prm_avg_term_next)-cell2mat(g_nodes_term))));
end
if (epsilon_prm_avg<=ops.primal_inf) %average_primal feasibility less&& details.restart<1
if(details.restart<1)
details.term_crit(1,1)=1;
details.iterate=j;
j=10*ops.steps;
%
else
if (min(min(min(W.y)),min( W_minyt))>0)
sum=0;
for i=1:Nd-Ns
sum=sum-W.y(i,:)*(prm_fes(:,i)-g_nodes(:,i));
end
for i=1:Ns
sum=sum-W.yt{i,:}*(prm_fes_term{i,1}-g_nodes_term{i,1});
end
if sum<=ops.dual_gap %condition 29. dual gap
details.term_crit(1,2)=1;
details.iterate=j;
j=10*ops.steps;
else
prm_cst=0;%primal cost;
for i=1:Nd-Ns
prm_cst=prm_cst+Tree.prob(i,1)*(Z.X(:,i)'*V.Q*Z.X(:,i)+Z.U(:,i)'*V.R*Z.U(:,i));
end
for i=1:Ns
prm_cst=prm_cst+Tree.prob(Tree.leaves(i))*(Z.X(:,Tree.leaves(i))'*V.Vf{i,1}*...
Z.X(:,Tree.leaves(i)));
end
if sum<=ops.dual_gap*prm_cst/(1+ops.dual_gap) %condition 30 dual gap
details.term_crit(1,3)=1;
details.iterate=j;
j=10*ops.steps;
else
%step 4: theta update
theta(1)=theta(2);
theta(2)=(sqrt(theta(1)^4+4*theta(1)^2)-theta(1)^2)/2;
j=j+1;
end
end
else
prm_cst=0;%primal cost;
dual_cst=0;% dual cost;
for i=1:Nd-Ns
prm_cst=prm_cst+Tree.prob(i,1)*(Z.X(:,i)'*V.Q*Z.X(:,i)+Z.U(:,i)'*V.R*Z.U(:,i));
dual_cst=dual_cst+Y.y1(i,:)*(prm_fes(:,i)-g_nodes(:,i));
end
for i=1:Ns
prm_cst=prm_cst+Tree.prob(Tree.leaves(i))*(Z.X(:,Tree.leaves(i))'*V.Vf{i,1}*...
Z.X(:,Tree.leaves(i)));
dual_cst=dual_cst+Y.yt1{i,:}*(prm_fes_term{i,1}-g_nodes_term{i,1});
end
if (-dual_cst<=ops.dual_gap*max(dual_cst,1)) %condtion 27 (dual gap)
details.term_crit(1,4)=1;
details.iterate=j;
j=10*ops.steps;
else
%step 4: theta update
theta(1)=theta(2);
theta(2)=(sqrt(theta(1)^4+4*theta(1)^2)-theta(1)^2)/2;
j=j+1;
end
end
end
%}
else
epsilon_prm=max( max(max(prm_fes-g_nodes)), ...
max(max(cell2mat(prm_fes_term)-cell2mat(g_nodes_term))) );
if(epsilon_prm<=ops.primal_inf) % primal feasibility of the iterate
if (min(min(min(W.y)),min( W_minyt))>0)
sum=0;
for i=1:Nd-Ns
sum=sum-W.y(i,:)*(prm_fes(:,i)-g_nodes(:,i));
end
for i=1:Ns
sum=sum-W.yt{i,:}*(prm_fes_term{i,1}-g_nodes_term{i,1});
end
if sum<=ops.dual_gap %condition 29. dual gap
details.term_crit(1,2)=1;
details.iterate=j;
j=10*ops.steps;
else
prm_cst=0;%primal cost;
for i=1:Nd-Ns
prm_cst=prm_cst+Tree.prob(i,1)*(Z.X(:,i)'*V.Q*Z.X(:,i)+Z.U(:,i)'*V.R*Z.U(:,i));
end
for i=1:Ns
prm_cst=prm_cst+Tree.prob(Tree.leaves(i))*(Z.X(:,Tree.leaves(i))'*V.Vf{i,1}*...
Z.X(:,Tree.leaves(i)));
end
if sum<=ops.dual_gap*prm_cst/(1+ops.dual_gap) %condition 30 dual gap
details.term_crit(1,3)=1;
details.iterate=j;
j=10*ops.steps;
else
%step 4: theta update
theta(1)=theta(2);
theta(2)=(sqrt(theta(1)^4+4*theta(1)^2)-theta(1)^2)/2;
j=j+1;
end
end
else
prm_cst=0;%primal cost;
dual_cst=0;% dual cost;
for i=1:Nd-Ns
prm_cst=prm_cst+Tree.prob(i,1)*(Z.X(:,i)'*V.Q*Z.X(:,i)+Z.U(:,i)'*V.R*Z.U(:,i));
dual_cst=dual_cst+Y.y1(i,:)*(prm_fes(:,i)-g_nodes(:,i));
end
for i=1:Ns
prm_cst=prm_cst+Tree.prob(Tree.leaves(i))*(Z.X(:,Tree.leaves(i))'*V.Vf{i,1}*...
Z.X(:,Tree.leaves(i)));
dual_cst=dual_cst+Y.yt1{i,:}*(prm_fes_term{i,1}-g_nodes_term{i,1});
end
if (-dual_cst<=ops.dual_gap*max(dual_cst,1)) %condtion 27 (dual gap)
details.term_crit(1,4)=1;
details.iterate=j;
j=10*ops.steps;
else
%step 4: theta update
theta(1)=theta(2);
theta(2)=(sqrt(theta(1)^4+4*theta(1)^2)-theta(1)^2)/2;
j=j+1;
end
end
else
%step 4: theta update
theta(1)=theta(2);
theta(2)=(sqrt(theta(1)^4+4*theta(1)^2)-theta(1)^2)/2;
j=j+1;
end
end
details.epsilon_prm_avg(iter)=epsilon_prm_avg;
details.epsilon_prm(iter)=epsilon_prm;
details.dual_cst(iter)=0;% dual cost
details.dual_grad(iter)=0; % dual gradient
for i=1:Nd-Ns
details.dual_cst(iter)=details.dual_cst(iter)+Y.y1(i,:)*(prm_fes(:,i)-g_nodes(:,i));
details.dual_grad(iter)=details.dual_grad(iter)+(prm_fes(:,i)-g_nodes(:,i))'*(Y.y1(i,:)-Y.y0(i,:))';
end
for i=1:Ns
details.dual_grad(iter)=details.dual_grad(iter)+(Y.yt1{i,1}-Y.yt0{i,1})*...
(prm_fes_term{i,1}-g_nodes_term{i,1});
details.dual_cst(iter)=details.dual_cst(iter)+Y.yt1{i,1}*(prm_fes_term{i,1}-g_nodes_term{i,1});
end
details.dual_cst(iter)=details.prm_cst(iter)-details.dual_cst(iter);
end
details.dual_gap=details.prm_cst(iter)-details.dual_cst(iter);
details.gpad_solve=toc;
%details.Q=Q;
details.W=W;
%details.epsilon_prm_avg= epsilon_prm_avg;
%details.epsilon_prm=epsilon_prm;
end