[Octave-bug-tracker] [bug #47314] optim package: quadprog() equality constraints have opposite sign

[Ray Zimmerman]

Follow-up Comment #16, bug #47314 (project octave):

I'm not sure I understand what you mean by "Matlab chooses to assign lambda of
too close upper and lower bounds to the lower bound". It would be incorrect to
always assign it to lower or always to upper. That depends on the problem.

I assume when the bounds are "too close" they are being replaced by an
equality constraint. In that case it is the the sign of the lambda from that
constraint that tells you which bound is binding, and therefore which bound to
assign the lambda too.

Here is a trivial example, run in Matlab, that illustrates.


>> [x,obj,flag,op,lambda]=quadprog(1,0,[],[],[],[],1,1+eps);    

Solution found during presolve.

Some combination of the bounds, linear constraints, and linear terms
in the objective function immediately lead to the solution.

>> lambda                                                   

lambda = 

    ineqlin: [0x1 double]
      eqlin: [0x1 double]
      lower: 1
      upper: 0

>> [x,obj,flag,op,lambda]=quadprog(1,0,[],[],[],[],-1-eps,-1);  

Solution found during presolve.

Some combination of the bounds, linear constraints, and linear terms
in the objective function immediately lead to the solution.

>> lambda                                                     

lambda = 

    ineqlin: [0x1 double]
      eqlin: [0x1 double]
      lower: 0
      upper: 1.0000


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