optimization using problem based

Hello!

i want to optimize the varibles so that i get the maximum valus of my function

i have 4 varibles (for now):

delta = optimvar('delta',1);
eta   = optimvar('eta',1);
alpha   = optimvar('alpha',1);
t   = optimvar('t',1,'LowerBound',0,'UpperBound',Time);

and this is my constrains:

T     = alpha*t^2+eta*t;
T_dot = 2*alpha*t+eta;
omega = delta*t;
%constrains
cons1 = T <= T_max;
cons2 = T >= T_min;
cons3 = omega <= omega_max;
cons4 = omega >= omega_min;
cons5 = T_dot <= T_dot_max;
cons6 = T_dot >= T_dot_min;

my questions

1. how do i make my temperature profile (T) to be lower that T_max and bigger than T_min for every value of the time (0<t<Time)?
2. i know i cant do it now (cause this is not a full second order profile), but if T was:

T     = alpha*t^2+eta*t+const;

how can i make the sulution start from T_min? something like initial condition so that T(0) = T_min

or: how can i make the solution go trough every value between T_min and T_max?

Thank u all!

this is the full code i'm using

%% General
clc;
clear;
close;
fontsize = {'Fontsize',14};
linewidth ={'Linewidth', 1.5};
legendfont = {'FontSize' , 12};
T_max = 60;
T_min = -60;
omega_max = 200;
omega_min = -200;
T_dot_max = 5;
T_dot_min = -5;
Time = 100;
%% Optimization problem
prob = optimproblem('ObjectiveSense','max');
%optimization varibles

delta = optimvar('delta',1);
eta   = optimvar('eta',1);
alpha   = optimvar('alpha',1);
t   = optimvar('t',1,'LowerBound',0,'UpperBound',Time);
%setting initial point
x0.delta = 0;
x0.eta   = 0;
x0.t     = 0;
x0.alpha = 0;
%profiles
T     = alpha*t^2+eta*t;
T_dot = 2*alpha*t+eta;
omega = delta*t;
%constrains
cons1 = T <= T_max;
cons2 = T >= T_min;
cons3 = omega <= omega_max;
cons4 = omega >= omega_min;
cons5 = T_dot <= T_dot_max;
cons6 = T_dot >= T_dot_min;
prob.Constraints.cons1 = cons1;
prob.Constraints.cons2 = cons2;
prob.Constraints.cons3 = cons3;
prob.Constraints.cons4 = cons4;
prob.Constraints.cons5 = cons5;
prob.Constraints.cons6 = cons6;
%cost func
alpha = 1; %Weight factor
prob.Objective  = (alpha^(2)*t^5)/5 + (alpha*eta*t^4)/2 + (delta^(2)*t^3)/3 + (eta^(2)*t^3)/3 + t;
%show and solve
show(prob)
sol = solve(prob,x0);

%% setting the profiles i get
dt = 1;
time       = 0:dt:sol.t;
T_opti     = sol.alpha.*time.^2+sol.eta.*time;
omega_opti = sol.delta.*time;
%% ploting
%omega profile
figure(1);
plot(time,omega_opti,linewidth{1:2});
xlabel('t [sec]');
ylabel('\omega [rad/s]');
grid on;
%temperature profile
figure(2);
plot(time,T_opti,'r',linewidth{1:2});
xlabel('t [sec]');
ylabel('T [\circC]');
grid on;
%both
figure(3);
yyaxis left
plot(time,omega_opti,linewidth{1:2});
xlabel('t [sec]');
ylabel('\omega [rad/s]');
ylim([omega_min omega_max]);
yyaxis right
grid on;
plot(time,T_opti,'r',linewidth{1:2});
xlabel('t [sec]');
ylabel('T [\circC]');
ylim([T_min T_max]);

Answer 1

[Matt J]

Are you sure t should be an optimvar? It seems to me it should be a set of discrete known values

t   = linspace(0,Time,N)

Once you make that change, and choose const=T_min, it seems to me everything is as you want it.

[eden meirovich]

first of all, thank u for your answer.

i tried what u said before, in that case, my Objective function look like that (just added the dots)

prob.Objective  = (alpha^(2).*t.^5)/5 + (alpha*eta.*t.^4)/2 + (delta^(2).*t.^3)/3 + (eta^(2).*t.^3)/3 + t;

and i get this error:

Error using optimization (line 49)

Objective must be a scalar OptimizationExpression or a struct containing a scalar

OptimizationExpression.

beacuse now prob.Objective is an 101X1 vector of optimization varibles (1 of every time step )

how can i handle this ?

[Matt J]

I can't tell what your objective is supposed to be when you have multiple time steps. Is it some sort of least squares criterion?

[eden meirovich]

well,it might be the one in the last time step, t=Time. ( in later problems it might no)

at the moment i have

6X length(t) Constraints, when i try to solve it for the last objective ( beacuse now i know the grater as t is bigger) i get this:

Solving problem using quadprog.

Your Hessian is not symmetric. Resetting H=(H+H')/2.

The interior-point-convex algorithm does not accept an initial point.

Ignoring X0.

The problem is non-convex.

and to sol is just [ 1 1 1] array.

which is clearly not correct, beacuse it's not satisfied all the Constraints

in the future i would like to max my objective , when i dont know which t is giving me the largest value (maybe i sould stop before t=Time? and "save time"), so it's look like i might have 101X1 objective function, and i would like to find the biggest one (this is why i used t as optimvar in the start)

is my answer helpd u?

thank u so much

[Matt J]

well,it might be the one in the last time step, t=Time.

If so, then,

prob.Objective  = (alpha^(2)*Time^5)/5 + (alpha*eta*Time^4)/2 +...
                  (delta^(2)*Time^3)/3 + (eta^(2)*Time^3)/3 + Time;

[eden meirovich]

thank u for the answer!

i have another question about this problem.

if i wish to make my temperature profile (T) go through all th range ( so go bewteen -60 to 60). how can i add this?