"fmincon" optimization with nonlinear constraints: colon error

Hello!

This is my second post for the same topic (solar production with an hourly resolution over 15 years), but I have a different question this time. Thanks in advance for the help! Here's the issue:

I have an objective function that I can solve with fmincon (I think), only one nonlinear equality constraint and variable bounds. My variable is Cpv and it will be a single number, not an array.

Function = @ObjFun3; %Saved in the same directory with filename=function name
nonlinconst = @PVnonlincon; %Saved in the same directory with filename=function name
[Cpv,fval] = fmincon(Function,10000,[],[],[],[],0,10000,nonlinconst); 

If I eliminate the nonlincon arguement, fmincon finds a solution (which is obviously not sufficient, I just wanted to check where the problem is). The error I am getting is:

Input arguments to function include colon operator. To input the colon
character, use ':' instead.

Error in fmincon (line 651)
    initVals.nceq = ceqtmp(:);

Error in Opt3 (line 29)
[Cpv,fval] = fmincon(Function,10000,[],[],[],[],0,10000,nonlinconst);

Do I have a conceptual error somewhere, or a command that I cannot use when declaring a function, or an argument that fmincon doesn't accept?

ObjFun3 is defined as:

function [OF] = ObjFun3(Cpv)
    DataW = struct2array(load('DataNinjaW+PV.mat','DataW')); %8760x15x6 array
    DataPV = struct2array(load('DataNinjaW+PV.mat','DataPV')); %8760x15x6 array
    Cn = 10000; 
    r = size(DataW,1);
    Pw = DataW(r,1,1); 
    N = Cn .* ones(size(Pw));
    NinjaPV = DataPV(r,1,Loc); 
     
        function F = Fed_pv(Cpv)
            F = min((NinjaPV.*Cpv/1000), (N-Pw));
        end
 
    OF = sum(N - Pw - Fed_pv(Cpv), 'all');
end

And PVnonlincon is defined as:

function [c_ineq,c_eq] = PVnonlincon(Cpv)
    DataW = struct2array(load('DataNinjaW+PV.mat','DataW')); %8760x15x6 array
    DataPV = struct2array(load('DataNinjaW+PV.mat','DataPV')); %8760x15x6 array
    Cn = 10000; 
    r = size(DataW,1);
    Pw = DataW(r,1,1); 
    N = Cn .* ones(size(Pw));
    NinjaPV = DataPV(r,1,Loc); 
    
    c_ineq = [ ];
    Anonymous = @(Cpv) Fed_Pv(Cpv) + NotFed(Cpv) - NinjaPV*(Cpv);
    c_eq = Anonymous;
    
    function NF = NotFed(Cpv)
        NF = max(0,(NinjaPV*Cpv/1000)+Pw-N);
    end
 
    function F = Fed_Pv(Cpv)
        F = min((NinjaPV*Cpv/1000), (N-Pw));
    end
end

[Matt J]

My variable is Cpv and it will be a single number, not an array.

If Cpv is a scalar, then fmincon is overkill. You should really just use fminbnd.

Also, I think there must be a mistake in your nonlinear constraints. Your equality constraint function "Anonymous" is piecewise linear in Cpv, which means it can only have a finite number of roots (at most 3 in this case) unless the slope of some piece is zero over some interval. But that doesn't look possible here unless you really meant,

 Anonymous = @(Cpv) Fed_Pv(Cpv) + NotFed(Cpv) - NinjaPV*(Cpv)/1000;

Answer 1

[Matt J]

You are returning a function handle in c_eq, when really you should be evaluating the function at Cpv,

c_eq = Anonymous(Cpv);

Aside from that, however, both your objective and constraints are non-differentiable functions, and so are outside the scope of what fmincon can handle. You should probably use ga() instead.

[Amalia Diaz]

Thank you! That fixed the colon error. And I also corrected the mistake you pointed out in the comment. It is sometimes frustrating to start using a new software, but at least you guys are there to point out the not-so-obvious-obvious things.

fminbnd is perhaps not an option, given the non-differentiable functions. I will try with ga(), although it's taking very long to find a solution with the same inputs and results in:

Optimization terminated: average change in the fitness value less than options.
FunctionTolerance and constraint violation is less than options.ConstraintTolerance.

[Matt J]

fminbnd is perhaps not an option

No, actually fminbnd shouldn't care about differentiability.

ga() can struggle with non-linear equality constraints, I seem to recall, and that may be why you see slow behavior. But there is no reason you should have non-linear constraints in a 1D minimization problem. In 1D, all relevant constraints can be expressed as simple upper and lower bounds, a<=x<=b.