optimization using solver based

hello!

i'm trying to use optimization tool box (problem based), and optimize 2 vector NX1 data potints.

omega = optimvar('omega',N,'LowerBound',omega_min,'UpperBound',omega_max);
T     = optimvar('T',N,'LowerBound',T_min,'UpperBound',T_max);

i have my constrains here on the lower bound and upper bound, and i have constrain on thegradient too:

%% 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;

and my cost function here.

one = ones(N,1);
prob.Objective  =  sum(omega(:).*omega(:))+sum(one)+sum(T(:).*T(:));
%show and solve
%show(prob)
x0.omega(1:N)=0;
x0.T(1:N)    =0;
sol = solve(prob,x0);
disp(sol);

when i run the code i get that: The problem is non-convex.

any idea what can i do to solve it?

full code:

%% General
clc;
clear;
close;
fontsize = {'Fontsize',14};
linewidth ={'Linewidth', 1.5};
legendfont = {'FontSize' , 12};
axissize = {'FontSize' , 12};
T_max = 60;
T_min = -60;
omega_max = 200;
omega_min = -200;
T_dot_max = 5;
T_dot_min = -5;
omega_dot_max = 10;
omega_dot_min = -10;
Time = 100;
dt=1;
N=100;
%% Optimization problem
prob = optimproblem('ObjectiveSense','max');
%optimization varibles - change here
omega = optimvar('omega',N,'LowerBound',omega_min,'UpperBound',omega_max);
T     = optimvar('T',N,'LowerBound',T_min,'UpperBound',T_max);

%t   = optimvar('t',1,'LowerBound',0,'UpperBound',Time);
t   = 0:dt:Time;
%setting initial point - change here
x0.T     =0 ;
x0.omega = 0;

%% 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;

%initial condition
cons7 = T(1)==-60;
prob.Constraints.cons7=cons7;
cons8 = omega(1)==0;
prob.Constraints.cons8=cons8;

%cost func
%w =10^-12 ;%Weight factor
one = ones(N,1);
prob.Objective  =  sum(omega(:).*omega(:))+sum(one)+sum(T(:).*T(:));
%show and solve
%show(prob)
x0.omega(1:N)=0;
x0.T(1:N)    =0;
sol = solve(prob,x0);
disp(sol);

[eden meirovich]

any ideas some one?

Answer 1

[Alan Weiss]

Try adding the following lines after your script has run:

options = optimoptions('fmincon','MaxIterations',1e4);
[sol,fval,exitflag,output] = solve(prob,x0,'Solver','fmincon','Options',options);

Alan Weiss

MATLAB mathematical toolbox documentation

[eden meirovich]

first off all thank u.

this do helping me (i increasd it even more) to get a solution, but it's looks like it's not the the corect one. i even plot the cost function over time, and it's not getting bigger over time.

any other tips?

Eden,

[Alan Weiss]

You can try different starting points. See Change the Initial Point and Local vs. Global Optima.

Alan Weiss

MATLAB mathematical toolbox documentation