optimization problem - problem using det funciton

Hello

i'm trying to solve an optimization problem with involve calcualte the det of a matrix (here it's the temp varible).

the temp operator work for me before with optimization varibles, but now there is a problem. i think it's involve with using a non-linear optimization varibles, such as the varible F.

the error i get:

Check for missing argument or incorrect argument data type in call to function 'det'.

Error in optimization_vector_form (line 82)

prob.Objective = det(temp);

any ideas?

Thank you

clc;
clear;
close all;
Time = 100;
dt=1;
N=Time/dt;
%% Optimization problem
prob = optimproblem('ObjectiveSense','max');
%optimization varibles 
omega = optimvar('omega',N,'LowerBound',w_min,'UpperBound',w_max);
T     = optimvar('T',N,'LowerBound',T_min,'UpperBound',T_max);

%% Constrains
for i=1:N-1
  cons1(i) = (T(i+1)-T(i))/dt >= T_dot_min;  
  cons2(i) = (T(i+1)-T(i))/dt <= T_dot_max;
  cons3(i) = (omega(i+1)-omega(i))/dt >= omega_dot_min;  
  cons4(i) = (omega(i+1)-omega(i))/dt <= omega_dot_max;
end

prob.Constraints.cons1 = cons1;
prob.Constraints.cons2 = cons2;
prob.Constraints.cons3 = cons3;
prob.Constraints.cons4 = cons4;
for i=1:N-1
  A(i) = omega(i)^2;
  B(i) = T(i)^2;
  C(i) = omega(i)*T(i);
  F(i) = omega(i)^2*T(i);
  G(i) = omega(i)*T(i)^2;
  H(i) = omega(i)^2*T(i)^2;
end
  
    D = sum(omega);
  E = sum(T);
  temp = [A.sum F.sum D C.sum;
          F.sum H.sum C.sum G.sum;
          D C.sum Time E;
          C.sum G.sum E B.sum]; 
  prob.Objective = det(temp);

Answer 1

[Alan Weiss]

The main problem is that det is not a Supported Operations on Optimization Variables and Expressions. For example,

x = optimvar('x',2,2);
y = det(x)

Check for incorrect argument data type or missing argument in call to function 'det'.

You should also learn to make more efficient optimization expressions. I rewrote some of your expressions using an indexing technique that enables vectorized addition and subtraction, removing your inefficient loops.

Time = 100;
dt = 1;
N = Time/dt;

w_min = 0; % I made up constants to get this to work
w_max = 10; % Put in your own constants
T_min = 1;
T_max = 100;
T_dot_min = -10;
T_dot_max = 10;
omega_dot_min = -1;
omega_dot_max = 1;
%% Optimization problem
prob = optimproblem('ObjectiveSense','max');
%optimization varibles 
omega = optimvar('omega',N,'LowerBound',w_min,'UpperBound',w_max);
T     = optimvar('T',N,'LowerBound',T_min,'UpperBound',T_max);

indces = 1:(N - 1); % This is the technique
%% Constrains
% for i=1:N-1
%   cons1(i) = (T(i+1)-T(i))/dt >= T_dot_min;  
%   cons2(i) = (T(i+1)-T(i))/dt <= T_dot_max;
%   cons3(i) = (omega(i+1)-omega(i))/dt >= omega_dot_min;  
%   cons4(i) = (omega(i+1)-omega(i))/dt <= omega_dot_max;
% end

cons1 = (T(indces + 1) - T(indces))/dt >= T_dot_min;
cons2 = (T(indces + 1) - T(indces))/dt <= T_dot_max;
cons3 = (omega(indces + 1) - omega(indces))/dt >= omega_dot_min;
cons4 = (omega(indces + 1) - omega(indces))/dt <= omega_dot_max;

prob.Constraints.cons1 = cons1;
prob.Constraints.cons2 = cons2;
prob.Constraints.cons3 = cons3;
prob.Constraints.cons4 = cons4;

% I also use indces here

% for i=1:N-1
%   A(i) = omega(i)^2;
%   B(i) = T(i)^2;
%   C(i) = omega(i)*T(i);
%   F(i) = omega(i)^2*T(i);
%   G(i) = omega(i)*T(i)^2;
%   H(i) = omega(i)^2*T(i)^2;
% end
A = omega(indces).^2;
B = T(indces).^2;
C = omega(indces).*T(indces);
F = (omega(indces).^2).*T(indces);
G = omega(indces).*(T(indces).^2);
H = omega(indces).^2.*(T(indces).^2);
  
D = sum(omega(indces));
E = sum(T(indces));
temp = [A.sum F.sum D C.sum;
      F.sum H.sum C.sum G.sum;
      D C.sum Time E;
      C.sum G.sum E B.sum];

To use the unsupportetd operation det, use fcn2optimexpr.

detexpr = fcn2optimexpr(@det,temp);
prob.Objective = detexpr;

Alan Weiss

MATLAB mathematical toolbox documentation

[eden meirovich]

Thank you, this was helpful.