[Octave-bug-tracker] [bug #64369] sqp does not handle qp info=2 properly

[Julien Bect]

URL:
  <https://savannah.gnu.org/bugs/?64369>

                 Summary: sqp does not handle qp info=2 properly
                   Group: GNU Octave
               Submitter: jbect
               Submitted: jeu. 29 juin 2023 20:32:03
                Category: Octave Function
                Severity: 3 - Normal
                Priority: 5 - Normal
              Item Group: Unexpected Error or Warning
                  Status: None
             Assigned to: None
         Originator Name: 
        Originator Email: 
             Open/Closed: Open
                 Release: stable
         Discussion Lock: Any
        Operating System: Any
           Fixed Release: None
         Planned Release: None


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Follow-up Comments:


-------------------------------------------------------
Date: jeu. 29 juin 2023 20:32:03     By: Julien Bect <jbect>
sqp does not handle qp info=2 properly.

In fact, when qp return with info=2, sqp simply issues a warning and then
continues as if nothing happened (cf lines 434-443):

    switch (info)
      case 2
        warning (id, "sqp: QP subproblem is non-convex and unbounded");
      case 3
        warning (id, "sqp: QP subproblem failed to converge in %d
iterations",
                 INFO.solveiter);
      case 6
        warning (id, "sqp: QP subproblem is infeasible");
        lambda = old_lambda;  # The return value was size 0x0 in this case.
    endswitch


The problem is that lambda is empty in this case, which implies a very
inelegant crash a few lines below, with the following cryptic error message:

error: operator *: nonconformant arguments (op1 is 3x6, op2 is 0x0)
error: called from
    sqp at line 482 column 9


This behaviour is unsatifactory IMHO, since 1) the user gets a very opaque
error message, and 2) the function does not return the best point found so
far.

A few possible and easy workarounds:

*Option 1*: Exit properly with a dedicated error code, for instance 105: QP
subproblem not convex.  (info=2 occurs, in the current implementation, when
the matrix is not positive definite)

*Option 2*: Proceed as in the case info=6, i.e., keep the previous vector of
Lagrange multipliers (lambda = old_lambda).

*Option 3*: Use option 2, but not more than, say, 10 times in a row.  After
that, fold back to option 1.







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