You are free to use gpuArray variables within your objective function, and in constraint functions in the case of fmincon. Unfortunately, you are required to ensure that inputs and outputs of these functions are CPU variables, and so you must do CPU/GPU transfers at the beginning and end of each call, killing a lot of the potential speed-up of the GPU. I have pointed out this weakness to Matlab staff and was told they would look into an enhancement.
Still, you can keep any large fixed data like matrices on the GPU throughout the optimization, and that will reduce the overhead. In the example below, I was able to get a 30% acceleration on the GPU using this approach, for sufficiently large problem size, N. Note that I would never normally recommend that you use the nonlinear constraint function in fmincon to implement linear constraints. In this case, though, it is a necessary workaround to get them implemented on the GPU.
function test
N=10000; %problem size
H=eye(N);
Aeq0=ones(1,N); %CPU copy
Aeq=Aeq0;
beq=1;
options=optimoptions(@fmincon,'Display','off','SpecifyObjectiveGradient',true,...
'SpecifyConstraintGradient',true);
x0=5*rand(N,1)+10;
%% Run on CPU
objfun=@(x) objective(x,H);
confun=@(x) linconFAKE(x,Aeq0,Aeq,beq);
tic;
fmincon(objfun,x0,[],[],[],[],[],[],confun,options);
toc
%Elapsed time is 18.771326 seconds.
%% Run on GPU
[H,Aeq,beq]=deal(gpuArray(H), gpuArray(Aeq), gpuArray(beq));
objfun=@(x) objective(x,H);
confun=@(x) linconFAKE(x,Aeq0,Aeq,beq);
tic;
fmincon(objfun,x0,[],[],[],[],[],[],confun,options);
toc
%Elapsed time is 12.546122 seconds.
end
function [f,g]=objective(x,H)
g=H*x(:);
f=(x.'*g)/2;
f=gather(f);
if nargout>1
g=gather(g);
end
end
function [c,ceq,g,geq]=linconFAKE(x,Aeq0,Aeq,beq)
c=[];
ceq=gather(Aeq*x-beq);
if nargout>2
g=[];
geq=Aeq0(:); %Use CPU copy
end
end
