[Octave-bug-tracker] [bug #64500] fmincon equality constraint handling - nz

[Liang Tang]

URL:
  <https://savannah.gnu.org/bugs/?64500>

                 Summary: fmincon equality constraint handling  - nz
                   Group: GNU Octave
               Submitter: lt1234
               Submitted: Mon 31 Jul 2023 10:23:31 PM UTC
                Category: Octave Forge Package
                Severity: 3 - Normal
                Priority: 5 - Normal
              Item Group: Feature Request
                  Status: None
             Assigned to: None
         Originator Name: lt1234
        Originator Email: 
             Open/Closed: Open
                 Release: 8.2.0 8.X Series Bug Fix Release 
         Discussion Lock: Any
        Operating System: Microsoft Windows
           Fixed Release: None
         Planned Release: None


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Follow-up Comments:


-------------------------------------------------------
Date: Mon 31 Jul 2023 10:23:31 PM UTC By: Liang Tang <lt1234>
This line below occurs six times in optim 1.6.2

nz = 200 * eps; # This is arbitrary. Accuracy of equality constraints.

I recommend that nz be controlled by the user through options.

To see the effect of nz, an example is provided.

fun=@(x) sum(x.^2); X0=[10 11]';
Aeq=[1 -1]; Beq=[0]; % X(1)-X(2)=0
Aieq=[]; Bieq=[];
lb=[1 1]'; ub=[12 12]'; 
[X, FVAL, CVG,  outp]= fmincon (fun, X0, Aieq, Bieq, Aeq, Beq, lb, ub,
nonlcon=[]); 

error: Initial parameters violate constraints.
error: called from
    __lm_feasible__ at line 93 column 5
    fmincon at line 456 column 24

% try to satisfy the constraint (it works this time but it is not always true)


fcn=@(x) Aeq*x-Beq; 
[X0, FVAL, INFO, OUTPUT, FJAC] = fsolve(fcn, X0);
[X, FVAL, CVG,  outp]= fmincon (fun, X0, Aieq, Bieq, Aeq, Beq, lb, ub,
nonlcon=[])

Depending on the complexity of fcn and options, fsolve may not result in a
solution that will meet 200*eps (4e-16) in fmincon.  We can continue to reduce
TolX & TolFun for fdolve.  But a possible approach seems to be to relax nz or
allow users to adjust nz as they wish (like TolX & TolFun).  I recommend the
latter.  Thanks.    










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