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Edit: Apologies, the question needs to be reworked, because I cannot reproduce the original problem using this code. I don't delete the question, in case someone is preparing an answer at the moment. I will repost an improved version of the question in the future.

I have a set of inequalities in $$x_0,x_2,x_3,x_4$$

Each inequality is of the form $$\max \{T_1,T_2,\dots\}<c$$

where each $T_i$ is of the form $$T_i = \sum_{i\neq j} c_{ij} x_i x_j + \sum_{i} d_i x_i$$

or is itself a maximum over several $T_i$.

When using

FindInstance 

on this system, windows titled "Abort Dynamic Evaluation" with two different messages start to open and close quickly. The word "Running..." from the main window disappears then, and all defined objects turn from black font to blue font. This has also caused the unpleasant problem that whenever I start Mathematica (not necessarily the problematic notebook), these windows open and close quickly (the problem stops a few minutes after starting Mathematica).

Questions:

  1. How can I get rid of the opening and closing "Abort Dynamic Evaluation" windows?

  2. How can I find a solution for my system of inequalities?

PS: The above mathematics is noted in LaTeX notation, but the input window did not accept it to be displayed as LaTeX formulae.

PS: The exact inequalities are:

{x0 < 0, x0 > -1, x1 < 1/256, x1 > 0, x2 < -(1/2), 
 x3 > -1, (1 + x0 + x1) (1 + x2) - x1 (1 + x3) < 
  0, -x1 + Max[
    Max[-1 - 3 x2, 1 + Min[x2, x3]] + 
     Max[Max[1 + 
         Min[x2, x3], -x1 (1 + x3) + (1 + x1) (1 + Min[x2, x3])] + 
       Max[-1 - 3 x2, -1 - (3 + x1) x2, 1 + Min[x2, x3]], 
      1 + Min[x2, x3]] + 
     Max[(1 + x0) (1 + 
         Min[x2, x3]), -x1 (1 + x3) + (1 + x0 + x1) (1 + 
          Min[x2, x3])], 
    Max[(1 + x0) (1 + Min[x2, x3]), -1 - 
       x3 + (2 + x0) (1 + Min[x2, x3]), -x1 (1 + x3) + (1 + x0 + 
          x1) (1 + Min[x2, x3]), -(1 + x1) (1 + x3) + (2 + x0 + 
          x1) (1 + Min[x2, x3])] + 
     Max[-2 - 4 x2, -1 - 3 x2, -1 - (3 + x1) x2, -2 - (4 + x1) x2, 
      1 + Min[x2, x3]]] + 
   Max[(1 + x0) (1 + Min[x2, x3]), -1 - 
     x3 + (2 + x0) (1 + Min[x2, x3]), -x1 (1 + x3) + (1 + x0 + 
        x1) (1 + Min[x2, x3]), -(1 + x1) (1 + x3) + (2 + x0 + x1) (1 +
         Min[x2, x3])] + 
   Max[-2 - 4 x2, -1 - 3 x2, -1 - (3 + x1) x2, -2 - (4 + x1) x2, 
    1 + Min[x2, x3]] + 4 (1 + Min[x2, x3]) > x0/
  2, -2 x1 + 
   Max[(1 + x0) (1 + Min[x2, x3]), -1 - 
     x3 + (2 + x0) (1 + Min[x2, x3]), -x1 (1 + x3) + (1 + x0 + 
        x1) (1 + Min[x2, x3]), -(1 + x1) (1 + x3) + (2 + x0 + x1) (1 +
         Min[x2, x3])] + 
   Max[-2 - 4 x2, -1 - 3 x2, -1 - (3 + x1) x2, -2 - (4 + x1) x2, 
    1 + Min[x2, x3]] + 4 (1 + Min[x2, x3]) > x0/2}

Here is the full Mathematica code, including the FindInstance call:

FindInstance[
 {x0 < 0, x0 > -1, x1 < 1/256, x1 > 0, x2 < -(1/2), 
  x3 > -1, (1 + x0 + x1) (1 + x2) - x1 (1 + x3) < 
   0, -x1 + 
    Max[Max[-1 - 3 x2, 1 + Min[x2, x3]] + 
      Max[Max[1 + 
          Min[x2, x3], -x1 (1 + x3) + (1 + x1) (1 + Min[x2, x3])] + 
        Max[-1 - 3 x2, -1 - (3 + x1) x2, 1 + Min[x2, x3]], 
       1 + Min[x2, x3]] + 
      Max[(1 + x0) (1 + 
          Min[x2, x3]), -x1 (1 + x3) + (1 + x0 + x1) (1 + 
           Min[x2, x3])], 
     Max[(1 + x0) (1 + Min[x2, x3]), -1 - 
        x3 + (2 + x0) (1 + Min[x2, x3]), -x1 (1 + x3) + (1 + x0 + 
           x1) (1 + Min[x2, x3]), -(1 + x1) (1 + x3) + (2 + x0 + 
           x1) (1 + Min[x2, x3])] + 
      Max[-2 - 4 x2, -1 - 3 x2, -1 - (3 + x1) x2, -2 - (4 + x1) x2, 
       1 + Min[x2, x3]]] + 
    Max[(1 + x0) (1 + Min[x2, x3]), -1 - 
      x3 + (2 + x0) (1 + Min[x2, x3]), -x1 (1 + x3) + (1 + x0 + 
         x1) (1 + Min[x2, x3]), -(1 + x1) (1 + x3) + (2 + x0 + 
         x1) (1 + Min[x2, x3])] + 
    Max[-2 - 4 x2, -1 - 3 x2, -1 - (3 + x1) x2, -2 - (4 + x1) x2, 
     1 + Min[x2, x3]] + 4 (1 + Min[x2, x3]) > x0/
   2, -2 x1 + 
    Max[(1 + x0) (1 + Min[x2, x3]), -1 - 
      x3 + (2 + x0) (1 + Min[x2, x3]), -x1 (1 + x3) + (1 + x0 + 
         x1) (1 + Min[x2, x3]), -(1 + x1) (1 + x3) + (2 + x0 + 
         x1) (1 + Min[x2, x3])] + 
    Max[-2 - 4 x2, -1 - 3 x2, -1 - (3 + x1) x2, -2 - (4 + x1) x2, 
     1 + Min[x2, x3]] + 4 (1 + Min[x2, x3]) > x0/2},
 {x0, x1, x2, x3}
 ]
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  • $\begingroup$ Please share the Mathematica code you are using. $\endgroup$ – rhermans Aug 2 at 10:16
  • $\begingroup$ Thank you for following up. I have added the code into my question. $\endgroup$ – user66834 Aug 2 at 11:15
  • 1
    $\begingroup$ Thank you for the code. It may or may not help you much, but if I haven't made a mistake then after a little thinking Version 12 returns {{x0 -> -1/2, x1 -> 1/512, x2 -> -1, x3 -> 0}} with the code you show above $\endgroup$ – Bill Aug 2 at 14:23
  • $\begingroup$ If you can no longer reproduce the error, it’s possible that the error was caused by a lingering definition that got cleared. This is often the source of temporary issues. $\endgroup$ – MassDefect Aug 3 at 16:47