Problem regarding fmincon solver

Hi,

I am trying to learn fmincon. I am trying to run the following example code for the first time. But, failed to run it. Getting error.

function [c,ceq] = nlcon (w)
c1 = 12*w(1) + 0*w(2) + w(5)*w(3) - 7*w(4) - 0.5*w(4);
c2 = - 0.5*w(4) - 12*w(1) - 0*w(2) - w(5)*w(3) + 7*w(4);
c = [c1;c2]
ceq = w(1) + w(2) + w(3) - w(4);
end

objective = @(w) w(1) + w(2) + 2*w(3) + 0*w(4) + 0*w(5);
x0 = [0.0,0.0,0.0,0.0,0.0];
disp(["Initial objective:" num2str(objective(x0))])
[c,ceq] = nlcon(x0)
A = [];
b = [];
Aeq = [];
beq = [];
lb = [0.0;0.0;0.0;2.0;1.0];
ub = [4.0;4.0;3.0;4.0;12.0];
nonlincon = @nlcon;
[x,fval] = fmincon(objective,x0,A,b,Aeq,beq,lb,ub,nonlincon)

But getting the error as follows:

܀error: Initial parameters violate constraints.

error: called from

__lm_feasible__ at line 92 column 5

fmincon at line 417 column 20

main at line 12 column 9

Could you please help me to solve this issue? Looking forward to your reply.

Answer 1

[Walter Roberson]

lb = [0.0;0.0;0.0;2.0;1.0];
ub = [4.0;4.0;3.0;4.0;12.0];
x0 = [0.0,0.0,0.0,0.0,0.0];

lb is lower bounds. Your second-last entry in lb is 2.0, so the second last entry in x0 must be at least 2.0, as in

x0 = [0.0,0.0,0.0,2.0,1.0];

[Sudip Poddar]

Thank you. I changed it. But, still getting same error:

error: Initial parameters violate constraints.

error: called from

__lm_feasible__ at line 92 column 5

fmincon at line 417 column 20

main at line 11 column 9

[Walter Roberson]

A = [];
b = [];
Aeq = [];
beq = [];
lb = [0.0;0.0;0.0;2.0;1.0];
ub = [4.0;4.0;3.0;4.0;12.0];

%x0 = [0.0,0.0,0.0,0.0,0.0];
x0 = lb;

objective = @(w) w(1) + w(2) + 2*w(3) + 0*w(4) + 0*w(5);
disp(["Initial objective:" num2str(objective(x0))])
[c,ceq] = nlcon(x0)


nonlincon = @nlcon;
[x,fval] = fmincon(objective,x0,A,b,Aeq,beq,lb,ub,nonlincon)

function [c,ceq] = nlcon (w)
c1 = 12*w(1) + 0*w(2) + w(5)*w(3) - 7*w(4) - 0.5*w(4);
c2 = - 0.5*w(4) - 12*w(1) - 0*w(2) - w(5)*w(3) + 7*w(4);
c = [c1;c2]
ceq = w(1) + w(2) + w(3) - w(4);
end

[Matt J]

Since the equality constraints are linear, I would recommend moving them to Aeq,beq.

A = [];
b = [];
Aeq = [ 1 1 1 -1 0];
beq = 0;
lb = [0.0;0.0;0.0;2.0;1.0];
ub = [4.0;4.0;3.0;4.0;12.0];

%x0 = [0.0,0.0,0.0,0.0,0.0];
x0 = lb;

objective = @(w) w(1) + w(2) + 2*w(3) + 0*w(4) + 0*w(5);
disp(["Initial objective:" num2str(objective(x0))])
[c,ceq] = nlcon(x0)


nonlincon = @nlcon;
[x,fval] = fmincon(objective,x0,A,b,Aeq,beq,lb,ub,nonlincon)

function [c,ceq] = nlcon (w)
c1 = 12*w(1) + 0*w(2) + w(5)*w(3) - 7*w(4) - 0.5*w(4);
c2 = - 0.5*w(4) - 12*w(1) - 0*w(2) - w(5)*w(3) + 7*w(4);
c = [c1;c2];
ceq = [];
end

[Sudip Poddar]

Many thanks. I changed again. But, receiving the same error:

ઑerror: Initial parameters violate constraints.

error: called from

__lm_feasible__ at line 92 column 5

fmincon at line 417 column 20

[Walter Roberson]

What release are you using? These days, the checks on initial point are closer to line 490

[Sudip Poddar]

Hi Matt,

I did it. But getting the following error:

error: linear equality constraints: wrong dimensions

error: called from

__linear_constraint_dimensions__ at line 34 column 5

fmincon at line 284 column 5

Hi Walter,

I am using MATLAB R2020a.

[Walter Roberson]

In R2020a, line 284 of fmincon is

verbosity = 2;

and column numbers are not mentioned in error messages except for the case of invalid characters such as ` appearing in the code.

I believe you are using Octave, not MATLAB.

[Sudip Poddar]

Hi Walter,

Sorry. I thoght that fmincon is same in both Matlab and Octave. Thats why I told you that I am using Matlab. My apologies. Is there any difference of fmincon solver in octave and Matlab? I dont know about it.

[Walter Roberson]

I do not know how fmincon works in Octave.

Octave is not just a copy of MATLAB: Octave is a work-alike that copied many parts of the library but was written from scratch. It just has to more-or-less follow the documentation for the MATLAB version but can have very different algorithms and very different bugs.

[Sudip Poddar]

But, is it also giving error in Matlab?

[Walter Roberson]

For the code I posted, the result is

>> violate_constraints
    "Initial objective:"    "0"


c =

   -15
    13


ceq =

    -2


Local minimum found that satisfies the constraints.

Optimization completed because the objective function is non-decreasing in 
feasible directions, to within the value of the optimality tolerance,
and constraints are satisfied to within the value of the constraint tolerance.

<stopping criteria details>

x =

          1.15886428965752
         0.841135710333056
       2.0004820803248e-08
          2.00000001999577
          2.19458332033105


fval =

          2.00000004000022

[Sudip Poddar]

Thanks Water for showing my mistake. Could you please let me know which version of Matlab you are using?

[Sudip Poddar]

Another thing, is there any way of forcing some variables as integer and few other vearibale as real?

[Walter Roberson]

R2020a.

When you use fmincon() it is not possible to force integer constraints. To use integer constraints, you generally need ga() .

Your objective itself is fairly simple and could be handled by https://www.mathworks.com/help/optim/ug/intlinprog.html intlinprog -- but intlinprog does not handle nonlinear constraints, so you cannot use that.

ga() handles integer constraints and nonlinear constraints. However, when you use integer constraints, it can only handle nonlinear inequality constraints and not nonlinear equality constaints, which is a problem for you as you have nonlinear equality and nonlinear inequality. However, if Matt J is correct about rewriting your nonlinear equality constraints, you should be able to get rid of those, in which case you would be able to use ga()

[Matt J]

Your objective itself is fairly simple and could be handled by intlinprog -- but intlinprog does not handle nonlinear constraints, so you cannot use that.

Except that notice that if w(3) or w(5) is fixed, the whole problem becomes a linear program. So, for example, if w(3) is supposed to be constrained to a finite set of integer values 1,...N, you could conceivably loop over N sub-problems corresponding to each possible value of w(3). Each sub-problem could be solved with intlinprog.

[Sudip Poddar]

Hi Walter,

Many many thanks to you for your detailed explanation. I will try to use ga(). Could you please let me know the full name of ga. Is it genetic algorithm?

Hi Matt,

Many many thanks to you also. I agree with your views completely. I will check it also. Thanks.

[Walter Roberson]

https://www.mathworks.com/help/gads/ga.html

[Matt J]

But note that intlinprog, when you can apply it, is generally more reliable than ga. So, if w(3) or w(5) are finite, discrete variables, then you will more reliably find the global minimum using the deomposition strategy that I mentioned.

[Walter Roberson]

ga() is not reliable for finding global minima.

[Sudip Poddar]

Hi Walter,

Thanks a lot for providing the link. I will check ga. Thanks again.

Hi Matt,

I agree with you. I will check it also. Many thanks to you also.