MATLAB: Setting nonlcon for fmincon / patternsearch as a matlabfunction

function handlenonlinconOptimization ToolboxSymbolic Math Toolbox

Hi everyone,
I am encountering some difficulties when trying to structure the nonlinear inequalities as inputs (for the "nonlcon" input in the function "patternsearch"), and I have referred to the matlab documentation on "Nonlinear Constraints" that says:
"Write a nonlinear constraint function as follows:"
c = @(x)[x(1)^2/9 + x(2)^2/4 - 1;
        x(1)^2 - x(2) - 1];
ceq = @(x)tanh(x(1)) - x(2);
nonlcon = @(x)deal(c(x),ceq(x));
Due to the requirements of my problem, I cannot (or don't know how to) prepare an explicit mfile or function handle for my system of nonlinear inequality constraints. This is because the system of nonlinear inequality constraints have been constructed using the Symbolic Toolbox because are very long and vary with every iteration. Hence I have tried to use "matlabFunction" to try to convert the equations (in as symbolic variables) to function handles as follows
a_sym=sym('a',[10 10]);
eqn_nonlin=sym(zeros(10,1));
for i=1:10
    eqn_nonlin(i)=mean(abs(eqn_sym{i}/2));
end
c=matlabFunction(vertcat(eqn_nonlin-1,-eqn_nonlin+0.8));
ceq=[];
nonlcon = @(a_sym)deal(c(a_sym),ceq(a_sym));
where "c" is a function of all the elements above the diagonal of "a_sym" (a total of 45 elements)
>> c
c =
function_handle with value:
@(a1_2,a1_3,a1_4,a1_5,a1_6,a1_7,a1_8,a1_9,a2_3,a2_4,a2_5,a2_6,a2_7,a2_8,a2_9,a3_4,a3_5,a3_6,a3_7,a3_8,a3_9,a4_5,a4_6,a4_7,a4_8,a4_9,a5_6,a5_7,a5_8,a5_9,a6_7,a6_8,a6_9,a7_8,a7_9,a8_9,a1_10,a2_10,a3_10,a4_10,a5_10,a6_10,a7_10,a8_10,a9_10)[abs(((a1_2.*(-5.249914648266426e-5)-a1_3.*5.250328005396799e-5-a1_4.*5.07598403480356e-5-a1_5.*5.156525926342894e-5-a1_6.*5.138443653182008e-5-a1_7.*5.191200741797726e-5-a1_8.*5    [truncated due to length]
It seems that this method of structuring the nonlinear inequality constraint is not correct beacuise I get an error when I try
>> nonlcon(ones(45,1))
Not enough input arguments.
Error in symengine>@(a1_2,a1_3,a1_4,a1_5,a1_6,a1_7,a1_8,a1_9,a2_3,a2_4,a2_5,a2_6,a2_7,a2_8,a2_9,a3_4,a3_5,a3_6,a3_7,a3_8,a3_9,a4_5,a4_6,a4_7,a4_8,a4_9,a5_6,a5_7,a5_8,a5_9,a6_7,a6_8,a6_9,a7_8,a7_9,a8_9,a1_10,a2_10,a3_10,a4_10,a5_10,a6_10,a7_10,a8_10,a9_10)[abs(((a1_2.*(-5.249914648266426e-5)-a1_3.*5.250328005396799e-5-a1_4.*5.07598403480356e-5-a1_5.*5.156525926342894e-5-a1_6.*5.138443653182008e-5-a1_7.*5.191200741797726e-5-a1_8.*5. [truncated due to length]
Error in @(a_sym)deal(c(a_sym),[])
or
>> nonlcon(1,2,3,4,5,6,7,8,9,0,...
          1,2,3,4,5,6,7,8,9,0,...
          1,2,3,4,5,6,7,8,9,0,...
          1,2,3,4,5,6,7,8,9,0,...
          1,2,3,4,5)
Error using @(a_sym)deal(c(a_sym),[])
Too many input arguments.
Would you please advice me on how I should structure the nonlinear inequalities from a symbolic variable?
Thank you very much. I appreciate your time and patience.

Best Answer

Create a wrapper function like the one below. To make it visible from the workspace where patternsearch is called, you can make it a local function or a nested function in the same file, rather than placing it in a separate mfile. Pass the function handle generated by matlabFunction to the wrapper as a fixed parameter:
cFun=matlabFunction(vertcat(eqn_nonlin-1,-eqn_nonlin+0.8));
nonlcon = @(a) nonlconWrapper(a,cFun); 
a_optimal = patternsearch(fun,a_Initial,A,b,Aeq,beq,lb,ub, nonlcon  );
function [c,ceq]=nonlconWrapper(a,cFun) %This can be a local function
   aCell=num2cell(a);
   c=cFun(aCell{:});
   ceq=[];
   
end
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