I'm trying to run a global optimization in Matlab using the global optimization toolbox. I am using the fmincon local optimizer as an input. I am able to successfully run the fmincon local optimizer, as well as the MultiStart global optimizer with this problem. However, when I try to set it up as a GlobalSearch, I get an error message.
Below is the code I am trying to use for the GlobalSearch:
%the functions is f(w) rather than f(x)
%constraints:
A = [1,0,0; 0,1,0; 0,0,1];
b = [.80, .80, .80];
Aeq = [1 1 1];
beq = 1;
lb = .10 * [1 1 1];
ub = .8 * [1 1 1];
w = [weight1, weight2, weight3];
wstart = randn(3,1);
options = optimset('Algorithm','interior-point');
% function handle for the objective function (note that variables
% aa through hh are additional parameters that the solver does not modify):
h = #(w)Difference_in_Returns(w(1),w(2),w(3), aa, bb, cc, dd, ee, ff, gg, hh);
% problem structure:
problem = createOptimProblem('fmincon','x0',wstart,'objective',h,'Aineq',A,...'
'bineq',b,'Aeq',Aeq,'beq',beq,'options',options,'lb',lb,'ub',ub);
gs = GlobalSearch;
run(gs,problem)
When I try to run this, Matlab bugs out and prints:
Error using -
Matrix dimensions must agree.
Error in C:\Program Files\MATLAB\R2012a\toolbox\globaloptim\globaloptim\private\
globalsearchnlp.p>i_calcConstrViolation (line 593)
Error in C:\Program Files\MATLAB\R2012a\toolbox\globaloptim\globaloptim\private\
globalsearchnlp.p>i_calcPenalty (line 627)
Error in C:\Program Files\MATLAB\R2012a\toolbox\globaloptim\globaloptim\private\
globalsearchnlp.p>globalsearchnlp (line 343)
Error in GlobalSearch/run (line 330)
[x,fval,exitflag,output] = ...
Error in Optimization_Setup (line 62)
run(gs,problem)
I believe the problem is outlined by the lines:
Error using -
Matrix dimensions must agree.
Error in GlobalSearch/run (line 330)
[x,fval,exitflag,output] = ...
Any tips are highly appreciated. Please let me know if you have any questions.
Related
I am not good at Matlab at all. I am trying to find minimum of function witjh constrains.
I am trying to use eample line by line as it is in documentation (https://www.mathworks.com/help/optim/ug/optimization-toolbox-tutorial.html - part Constrained Optimization Example: User-Supplied Gradients)
I have tried following code:
f = #(x,y) x.*exp(-x.^2-y.^2)+(x.^2+y.^2)/20;
g = #(x,y) x.*y/2+(x-2).^2+(y-2).^2/2-4;
x0 = [2 ,0];
options = optimoptions('fmincon','Algorithm','interior-point','Display','iter');
gfun = #(x,y) deal(g(x,y),[]);
[x,fval,exitflag,output] = fmincon(f,x0,[],[],[],[],[],[],gfun,options);
And this is the console output:
>> Untitled4
Not enough input arguments.
Error in Untitled4>#(x,y)x.*exp(-x.^2-y.^2)+(x.^2+y.^2)/20 (line 1)
f = #(x,y) x.*exp(-x.^2-y.^2)+(x.^2+y.^2)/20;
Error in fmincon (line 552)
initVals.f = feval(funfcn{3},X,varargin{:});
Error in Untitled4 (line 7)
[x,fval,exitflag,output] = fmincon(f,x0,[],[],[],[],[],[],gfun,options);
Caused by:
Failure in initial objective function evaluation. FMINCON cannot continue.
I don't understand - what is wrong with my function?
you missed the part in the documentation defining fun,
and you miss-defined gfun.
(it is important that both are functions of a single variable, x)
Here is working code:
f = #(x,y) x.*exp(-x.^2-y.^2)+(x.^2+y.^2)/20;
g = #(x,y) x.*y/2+(x-2).^2+(y-2).^2/2-4;
x0 = [2 0];
options = optimoptions('fmincon','Algorithm','interior-point','Display','iter');
fun = #(x) f(x(1),x(2));
gfun = #(x) deal(g(x(1),x(2)),[]);
[x,fval,exitflag,output] = fmincon(fun,x0,[],[],[],[],[],[],gfun,options);
I am trying to solve the equation below for array d. I have used the snippet below:
channel_size = 9e-3;
d = [11e-3, 12e-3];
sigma = 0.49;
ee = 727/9806.65;
alpha = d-channel_size;
sym('p',[1 2])
for i = 1:2
eqn = alpha == (4.3^(1/7))*(p^(3/11))*(((1-(sigma^2))/ee)^(7/5))/(d.^(1/6))
S = solve(eqn, p)*0.015;
vpa(S/13e-12)
end
In fact, I should get two number corresponding to d(1) and d(2), but it does not work and this error appears:
Error using mupadmex
Error in MuPAD command: Operands are invalid. [linalg::matlinsolve]
Error in sym/privBinaryOp (line 1693)
Csym = mupadmex(op,args{1}.s, args{2}.s, varargin{:});
Error in sym/mrdivide (line 232)
X = privBinaryOp(A, B, 'symobj::mrdivide');
Declaring (d.^(1/6)) is wrong and instead (d(i)^(1/6)) should be used. In addition, as alpha = d-channel_size, in the equation, I should also declare alpha(i) instead of simple alpha.
I'm trying to solve a symbolic optimization problem using PSO optimizer in MATLAB. The variables r x a c n theta z are symbolic and CD is calculated by integrating r.
The CD is the objective function with free variables a,n, theta and lb and ub are bounds. Full code is as follows:
syms r x a c n theta z
assume(n,'positive');
D=0.24;
L=2;
f=L/D;
b=.8;
a0=0.02;
db=0.05;
V=1;
Re=(V*(D/2))/0.000001;
Cf=(0.075/(((log10(Re))-2)^2))+0.00025;
% Define r(x)
c=L-a-b-a0;
r1=0.5*D*(2*x/a)^(1/n);
I1=simplify(int(2*pi*r1,x,a0,a));
r2=D/2;
I2=simplify(int(2*pi*r2,x,a,a+b));
r3=(0.5*D)-((((3*D)/(2*(c)^2))-(tan(theta)/c))*(x-a-b)^2)+(((D/c^3 ...
(tand(theta)/c^2))*(x-a-b)^3);
I3=simplify(int(2*pi*r3,x,a+b,L));
A=simplify(I1+I2+I3);
Sn=pi*(D^2/4);
Cdstar=Cf*(1+(60*f^-3 )+(0.0025*f))*(A/(L^2));
Cdb=0.029*((db/D)^3)*(Cdstar^-0.5)*(Sn/(L^2));
CD=simplify(Cdstar+Cdb);
%optimization problem
objective=matlabFunction(CD,'Vars',[a,n,theta])
nVar=3;
lb = [deg2rad(5),0.25,a0];
ub = [deg2rad(60),5,L/2];
options =
optimoptions('particleswarm','SwarmSize',100,'HybridFcn',#fmincon);
[z,fval,exitflag,output] = particleswarm(objective,nVar,lb,ub,options)
And this is the error I get:
#(a,n,theta)pi.*4.404634153141517e-4+pi.*1.0./sqrt(pi.4.404634153141517e-4-pi.(a.*5.0-6.0).*1.0./(a.5.0e+1-5.9e+1).^3.(a.*2.32335e+6+tan((theta.*pi)./1.8e+2).*4.779e+6-tan(theta).*6.2658e+6-a.^2.*tan(theta).*2.655125e+7+a.^3.*tan(theta).*1.4875e+7-a.^4.*tan(theta).*3.125e+6-a.*tan((theta.*pi)./1.8e+2).*1.59975e+7+a.*tan(theta).*2.1063e+7+a.^2.*tan((theta.*pi)./1.8e+2).*2.008125e+7-a.^3.*tan((theta.*pi)./1.8e+2).*1.1203125e+7+a.^4.*tan((theta.*pi)./1.8e+2).*2.34375e+6-a.^2.*1.98e+6+a.^3.*5.625e+5-9.08811e+5).*1.223509486983755e-5-(n.pi.((a.*2.5e+1).^(-1.0./n)-2.0.^(1.0./n+1.0).*a.*2.5e+1).*1.101158538285379e-5)./(n+1.0)).9.440104166666668e-7-pi.(a.*5.0-6.0).*1.0./(a.5.0e+1-5.9e+1).^3.(a.*2.32335e+6+tan((theta.*pi)./1.8e+2).*4.779e+6-tan(theta).*6.2658e+6-a.^2.*tan(theta).*2.655125e+7+a.^3.*tan(theta).*1.4875e+7-a.^4.*tan(theta).*3.125e+6-a.*tan((theta.*pi)./1.8e+2).*1.59975e+7+a.*tan(theta).*2.1063e+7+a.^2.*tan((theta.*pi)./1.8e+2).*2.008125e+7-a.^3.*tan((theta.*pi)./1.8e+2).*1.1203125e+7+a.^4.*tan((theta.*pi)./1.8e+2).*2.34375e+6-a.^2.*1.98e+6+a.^3.*5.625e+5-9.08811e+5).*1.223509486983755e-5-(n.pi.((a.*2.5e+1).^(-1.0./n)-2.0.^(1.0./n+1.0).*a.*2.5e+1).*1.101158538285379e-5)./(n+1.0)
Not enough input arguments.
Error in
symengine>#(a,n,theta)pi.*4.404634153141517e-4+pi.*1.0./sqrt(pi.4.404634153141517e-4-pi.(a.*5.0-6.0).*1.0./(a.5.0e+1-5.9e+1).^3.(a.*2.32335e+6+tan((theta.*pi)./1.8e+2).*4.779e+6-tan(theta).*6.2658e+6-a.^2.*tan(theta).*2.655125e+7+a.^3.*tan(theta).*1.4875e+7-a.^4.*tan(theta).*3.125e+6-a.*tan((theta.*pi)./1.8e+2).*1.59975e+7+a.*tan(theta).*2.1063e+7+a.^2.*tan((theta.*pi)./1.8e+2).*2.008125e+7-a.^3.*tan((theta.*pi)./1.8e+2).*1.1203125e+7+a.^4.*tan((theta.*pi)./1.8e+2).*2.34375e+6-a.^2.*1.98e+6+a.^3.*5.625e+5-9.08811e+5).*1.223509486983755e-5-(n.pi.((a.*2.5e+1).^(-1.0./n)-2.0.^(1.0./n+1.0).*a.*2.5e+1).*1.101158538285379e-5)./(n+1.0)).9.440104166666668e-7-pi.(a.*5.0-6.0).*1.0./(a.5.0e+1-5.9e+1).^3.(a.*2.32335e+6+tan((theta.*pi)./1.8e+2).*4.779e+6-tan(theta).*6.2658e+6-a.^2.*tan(theta).*2.655125e+7+a.^3.*tan(theta).*1.4875e+7-a.^4.*tan(theta).*3.125e+6-a.*tan((theta.*pi)./1.8e+2).*1.59975e+7+a.*tan(theta).*2.1063e+7+a.^2.*tan((theta.*pi)./1.8e+2).*2.008125e+7-a.^3.*tan((theta.*pi)./1.8e+2).*1.1203125e+7+a.^4.*tan((theta.*pi)./1.8e+2).*2.34375e+6-a.^2.*1.98e+6+a.^3.*5.625e+5-9.08811e+5).*1.223509486983755e-5-(n.pi.((a.*2.5e+1).^(-1.0./n)-2.0.^(1.0./n+1.0).*a.*2.5e+1).*1.101158538285379e-5)./(n+1.0)
Error in particleswarm>makeState (line 694)
firstFval = objFcn(state.Positions(1,:));
Error in particleswarm>pswcore (line 169) state =
makeState(nvars,lbMatrix,ubMatrix,objFcn,options);
Error in particleswarm (line 151) [x,fval,exitFlag,output] =
pswcore(objFcn,nvars,lbRow,ubRow,output,options);
Error in MYRING_SYMS_optimisation_K (line 56) [z,fval,exitflag,output]
= particleswarm(objective,nVar,lb,ub,options)
Caused by:
Failure in initial objective function evaluation. PARTICLESWARM cannot continue.
The fun takes only one argument, which is a vector with nvars elements. From particleswarm doc:
x = particleswarm(fun,nvars) attempts to find a vector x that achieves a local minimum of fun. nvars is the dimension (number of design variables) of fun.
So you need to declare a new objective function that only takes 1 argument:
[z,fval,exitflag,output] = particleswarm( ...
#(x) objective(x(1), x(2), x(3)), ...
nVar,lb,ub,options)
i try to run the following in order to integrate numerically:
nu = 8;
psi=-0.2;
lambda = 1;
git = #(u) tpdf((0 - lambda * skewtdis_inverse(u, nu, psi)), nu);
g(t,i) = integral(git,1e-10,1-1e-10,'AbsTol',1e-16);
where tpdf is a matlab function and skewtdis:inverse looks like this:
function inv = skewtdis_inverse(u, nu, lambda)
% PURPOSE: returns the inverse cdf at u of Hansen's (1994) 'skewed t' distribution
c = gamma((nu+1)/2)/(sqrt(pi*(nu-2))*gamma(nu/2));
a = 4*lambda*c*((nu-2)/(nu-1));
b = sqrt(1 + 3*lambda^2 - a^2);
if (u<(1-lambda)/2);
inv = (1-lambda)/b*sqrt((nu-2)./nu)*tinv(u/(1-lambda),nu)-a/b;
elseif (u>=(1-lambda)/2);
inv = (1+lambda)/b*sqrt((nu-2)./nu).*tinv(0.5+1/(1+lambda)*(u-(1-lambda)/2),nu)-a/b;
end
What i get out is:
Error in skewtdis_inverse (line 6)
c = gamma((nu+1)/2)/(sqrt(pi*(nu-2))*gamma(nu/2));
Output argument "inv" (and maybe others) not assigned during call to "F:\Xyz\skewtdis_inverse.m>skewtdis_inverse".
Error in #(u)tpdf((0-lambda*skewtdis_inverse(u,nu,psi)),nu)
Error in integralCalc/iterateScalarValued (line 314)
fx = FUN(t);
Error in integralCalc/vadapt (line 133)
[q,errbnd] = iterateScalarValued(u,tinterval,pathlen);
Error in integralCalc (line 76)
[q,errbnd] = vadapt(#AtoBInvTransform,interval);
Error in integral (line 89)
Q = integralCalc(fun,a,b,opstruct);
If i , however call the function in thr handle directly there are no Problems:
tpdf((0 - lambda * skewtdis_inverse(1e-10, nu, psi)), nu)
ans =
1.4092e-11
tpdf((0 - lambda * skewtdis_inverse(1-1e-10, nu, psi)), nu)
ans =
7.0108e-10
Your effort is highly appreciated!
By default, integral expects the function handle to take a vector input.
In your code, the if-statement creates a complication since the condition will evaluate to true only if all elements of u satisfy it.
So, if u is a vector that has elements both greater than and less than (1-lambda)/2, inv will never be assigned.
There are two options:
Put the if-statement in a for-loop and iterate over all of the elements of u.
Use logical indexes for the assignment.
The second option is faster for large element count and, in my opinion, cleaner:
inv = u; % Allocation
IsBelow = u < (1-lambda)/2; % Below the threshold
IsAbove = ~IsBelow ; % Above the threshold
inv(IsBelow) = (1-lambda)/b*sqrt((nu-2)./nu)*tinv(u(IsBelow)/(1-lambda),nu)-a/b;
inv(IsAbove) = (1+lambda)/b*sqrt((nu-2)./nu)*tinv(0.5+1/(1+lambda)*(u(IsAbove)-(1-lambda)/2),nu)-a/b;
I am using numerical integration in MATLAB, with one varibale to integrate over but the function also contains a variable number of terms depending on the dimension of my data. Right now this looks like the following for the 2-dimensional case:
for t = 1:T
fxt = #(u) exp(-0.5*(x(t,1)-theta*norminv(u,0,1)).^2) .* ...
exp(-0.5*(x(t,2) -theta*norminv(u,0,1)).^2);
f(t) = integral(fxt,1e-4,1-1e-4,'AbsTol',1e-3);
end
I would like to have this function flexible in the sense that there could be any number of data points in, each in the following term:
exp(-0.5*(x(t,i) -theta*norminv(u,0,1)).^2);
I hope this is understandable.
If x and u have a valid dimension match (vector-vector or array-scalar) for the subtraction, you can put the whole matrix x into the handle and pass it to the integral function using the name-parameter pair ('ArrayValued',true):
fxt = #(u) exp(-0.5*(x - theta*norminv(u,0,1)).^2) .* ...
exp(-0.5*(x - theta*norminv(u,0,1)).^2);
f = integral(fxt,1e-4,1-1e-4,'AbsTol',1e-3,'ArrayValued',true);
[Documentation]
You may need a loop if integral ever passes a vector u into the handle.
But in looking at how the integral function is written, the integration nodes are entered as scalars for array-valued functions, so the loop shouldn't be necessary unless some weird dimension-mismatch error is thrown.
Array-Valued Output
In response to the comments below, you could try this function handle:
fx = #(u,t,k) prod(exp(-0.5*(x(t,1:k)-theta*norminv(u,0,1)).^2),2);
Then your current loop would look like
fx = #(u,t,k) prod(exp(-0.5*(x(t,1:k)-theta*norminv(u,0,1)).^2),2);
k = 2;
for t = 1:T
f(t) = integral(#(u)fx(u,t,k),1e-4,1-1e-4,'AbsTol',1e-3,'ArrayValued',true);
end
The ArrayValued flag is needed since x and u will have a dimension mismatch.
In this form, another loop would be needed to sweep through the k indexes.
However, we can improve this function by skipping the loop altogether since each iterate of the loop is independent by using the ArrayValued mode:
fx = #(u,k) prod(exp(-0.5*(x(:,1:k)-theta*norminv(u,0,1)).^2),2);
k = 2;
f = integral(#(u)fx(u,k),1e-4,1-1e-4,'AbsTol',1e-3,'ArrayValued',true);
Vector-Valued Output
If ArrayValued is not desired, which may be the case if the integration requires a lot of subdivisions and a vector-valued u is preferable, you can also try a recursive version of the handle using cell arrays:
% x has size [T,K]
fx = cell(K,1);
fx{1} = #(u,t) exp(-0.5*(x(t,1) - theta*norminv(u,0,1)).^2);
for k = 2:K
fx{k} = #(u,t) fx{k-1}(u,t).*exp(-0.5*(x(t,k) - theta*norminv(u,0,1)).^2);
end
f(T) = 0;
k = 2;
for t = 1:T
f(t) = integral(#(u)fx{k}(u,t),1e-4,1-1e-4,'AbsTol',1e-3);
end
ThanksTroy but now I run into the follwing:
x = [0.3,0.8;1.5,-0.7];
T = size(x,1);
k = size(x,2);
theta= 1;
fx = #(u,t,k) prod(exp(-0.5*(x(t,1:k) - theta*norminv(u,0,1))^2));
for t = 1,T
f(t) = integral(#(u)fx(u,t,k),1e-4,1-1e-4,'AbsTol',1e-3);
end
Error using -
Matrix dimensions must agree.
Error in #(u,t,k)prod(exp(-0.5*(x(t,1:k)-theta*norminv(u,0,1))^2))
Error in #(u)fx(u,t,k)
Error in integralCalc/iterateScalarValued (line 314)
fx = FUN(t);
Error in integralCalc/vadapt (line 133)
[q,errbnd] = iterateScalarValued(u,tinterval,pathlen);
Error in integralCalc (line 76)
[q,errbnd] = vadapt(#AtoBInvTransform,interval);
Error in integral (line 89)
Q = integralCalc(fun,a,b,opstruct);