Why FindMinimum crashes the kernel in specific situation

Question

Bug introduced in 11.0.0 and fixed in 11.1

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I have found that FindMinimum crahses is a certain situation. Here is my minimal working example:

length = 50;
roundoffErrorMatrix = 
  10^-10*(# + Transpose@# &@RandomReal[{-1, 1}, {length, length}]);
costMatrix = IdentityMatrix@length + roundoffErrorMatrix;
variables = Table[Unique[], {i, 1, length}];

FindMinimum[{variables.costMatrix.variables, Thread[variables >= -1]},
  variables]

FindMinimum[{x^2, x >= -1}, x]

Explanation of code

In the minimal working example there two calls to FindMinimum. The second call is just a simple example to show some bad behavior that happens; I will explain more after discussing the first call to FindMinimum.

The first call to FindMinimum just basically minimizes the square length of a vector (since costMatrix is essentially the identity matrix), subject to the constraint that the components are all greater than -1.

To set up the first call to FindMinimum, I first pick length which gives the dimensionality of the minimization problem. Then I make a simulated round off error matrix, which is necessary to reproduce the error. Then I set my costMatrix equal to this round off error matrix plus the identity matrix. Lastly, I create an array for the variables for FindMinimum.

Description of Behavior

Now I will describe what happens when I run the code. I have the code in three cells: the setup, and the two calls to FindMinimum. The first cell runs just fine. When I run the second cell (first call to FindMinimum) for the first time, it does just fine.

After running the second cell once, I can do two things, both of which crash the kernel. The first thing I can do is to repeatedly run the second cell again. The other thing that crashes the kernel is to run the third cell once.

Necessary conditions

There are a surprising number of conditions for this bug to occur. There are three by my count:

1. The dimensionality of the problem (length) must be greater or equal to 50.

2. The costMatrix must have the round off error included. Simply IdentityMatrix or N@IdentityMatrix will not do.

3. The constraints must be present.

I am using Mathematica 11.0.0.0 on Linux x86 (64 bit). Why does this crash occur, and what is a good workaround?

Answer 1

Update: This bug has been fixed in the just released Mathematica 11.1.

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A good workaround was suggested by ilian.

For a workaround, please try Method -> "InteriorPoint".

This workaround worked for me. In particular, I can now run the first FindMinimum command for the code listing in my question as many times as I want, and the second FindMinimum command does not cause a crash either. Even better, the solution found with this option seems to be more accurate. I also did not notice a slow down when I applied this workaround to the original application.