How do i use optimization toolbox to optimize an objective function with matrix input variables (4x4)

I have an objective function and non linear constraint m file as follows:

objective function

function k = mut(u)
load('matlab1.mat')
k = (exp(u(1)*test__TT*u(2)));
end

non linear constraint

function [c,ceq] = constr(u)
load('matlab1.mat')
% Nonlinear inequality constraints
c = (exp(u(1)*test__TT*u(2)))-B;
ceq = [];
end
% End of function

test_TT input variable is a 4x4 matrix

i am solving using the optimization tool box "fmincon". u0 = [0 0]

when i run the optimization solver, i get an error saying "Supplied objective function must return a scalar value."

basically, my output should be two (4x4) optimal variables for u(1) and u(2).

how to i setup the problem to return solution thats calculates the optimal for each variable matrix pair (element wise).

Answer 1

[Alan Weiss]

You can only optimize scalar objective functions. What does it mean to optimize two or more functions at the same time? Either optimize each function separately, or find a Pareto front for a multiobjective optimization.

In terms of programming efficiency, you should not put a load statement in an objective function or nonlinear constraint function. Instead, load the data into your workspace just once, and then pass parameters using anonymous functions or nested functions as you prefer.

Alan Weiss

MATLAB mathematical toolbox documentation

[adewale oduwole]

to better rephrase my question, i would i return my decision variable 'u' as a 4x4 output argument in the optimization toolbox. or how do i define 'u' as a 4x4 matrix so matlab knows i need all values of 'u' that satisfies my function at minimun.

[Walter Roberson]

You cannot return a 4 x 4 output from your objective function to fmincon or related functions.

Now, if u is the input which is to be found, and a computation on u results in a scalar output of fitness, then you can use it. See https://www.mathworks.com/help/optim/ug/matrix-arguments.html . The output from fmincon will be the matrix of values that optimized the function.

[adewale oduwole]

i got matlab to reburn the matrix as a 4x4 by defining the u variable as u=u(:,:). but to solve my original problem which is a multivariable function, with u(n)..how to i formulate the start points for all u(n) to obtain individual outputs for all.

[Walter Roberson]

Does your objective function take multiple inputs and return a scalar output? If so, then don't worry about it: just pass in a matrix for the initial values of the variable and you will get out a matrix of the same size, and your objective function will be passed the variable in the form of a matrix.

Does your objective function return a non-scalar output? If so then that cannot be handled by MATLAB using fmincon or ga or particleswarm or patternsearch or simulated annealing. It can be handled by gamultiobj() though.