[Bonmin] another unexpected infeasible problem !

[Nicolas BERGER]

Bonjour à nouveau,


I am trying to solve the following problem (it is an optimisation problem
--"gear4"-- from MINLPlib which I have changed into a simple constraint
satisfaction problem) :

----------------------------------------------------------------
param best_value := 1.643428;
param eps        := 1; 		#= max(1, 1% x best_value)

var i1 integer >= 10 <= 25 ; #solu=19.0000000000,
var i2 integer >= 0 <= 20 ;  #solu=16.0000000000,
var i3 integer >= 37 <= 50 ; #solu=43.0000000000,
var i4 integer >= 45 <= 55 ; #solu=49.0000000000,
var x6 >= 0 <= 100 ; #solu=,
var x7 >= 0 <= 100 ; #solu=1.64342800000;


subject to
    cons1:-1.0e6*i1*i2/(i3*i4)-x6+x7=-144279.32477276;
    obj1:-x6-x7-(0) >= - best_value - eps;
    obj2:-x6-x7-(0) <= - best_value + eps;

option solver bonmin ;

solve ;
display i1,i2,i3,i4,x6,x7;
----------------------------------------------------------------




Here is what I get from Ampl :

-----------------------------------------------------------------
WARNING: Tried to set option "expect_infeasible_problem" to a value of "yes",
         but the previous value is set to disallow clobbering.
         The setting will remain as: "expect_infeasible_problem no"
WARNING: Tried to set option "mu_strategy" to a value of "adaptive",
         but the previous value is set to disallow clobbering.
         The setting will remain as: "mu_strategy monotone"
WARNING: Tried to set option "mu_oracle" to a value of "probing",
         but the previous value is set to disallow clobbering.
         The setting will remain as: "mu_oracle quality-function"
bonmin:

******************************************************************************
This program contains Ipopt, a library for large-scale nonlinear
optimization.
 Ipopt is released as open source code under the Common Public License (CPL).
         For more information visit http://projects.coin-or.org/Ipopt
******************************************************************************

Error in an AMPL evaluation. Run with "halt_on_ampl_error yes" to see
details.
IpOp0008I
              Num      Status      Obj             It       time
IpOp0009I     1        OPT         0              17       0.012001
Cbc0013I At root node, 0 cuts changed objective from 0 to 0 in 1 passes
Cbc0014I Cut generator 0 (Outer Approximation Supporting Hyperplanes for
NLP optimum) - 0 row cuts (0 active), 0 column cuts
Cbc0014I Cut generator 1 (GMI) - 1 row cuts (0 active), 0 column cuts
Cbc0014I Cut generator 2 (Probing) - 0 row cuts (0 active), 1 column cuts
Cbc0014I Cut generator 3 (covers) - 0 row cuts (0 active), 0 column cuts
Cbc0014I Cut generator 4 (MIR) - 0 row cuts (0 active), 0 column cuts
Cbc0014I Cut generator 5 (Outer Approximation local enumerator) - 0 row
cuts (0 active), 0 column cuts
Cbc0014I Cut generator 6 (Outer Approximation feasibility checker) - 0 row
cuts (0 active), 0 column cuts
Cbc0001I Search completed - best objective 1e+50, took 1 iterations and 0
nodes (0.42 seconds)

        "Finished"
Finished

bonmin: Infeasible problem
i1 = 0
i2 = 0
i3 = 0
i4 = 0
x6 = 0
x7 = 0
----------------------------------------------------------------




This problem is said to be infeasible, but it *DOES* have a solution when
I use my constraint satisfaction tool (RealPaver) :

-------------------------------------------------------------------
problem pb_gear4 /*MINLPlib*/
  num
    best_value := 1.643428,
    eps        := 1;

  var
    i1 : int ~ [10, 25] /*19.0000000000*/,
    i2 : int ~ [0, 20] /*16.0000000000*/,
    i3 : int ~ [37, 50] /*43.0000000000*/,
    i4 : int ~ [45, 55] /*49.0000000000*/,
    x6 : real ~ [0, 100] /**/,
    x7 : real ~ [0, 100] /*1.64342800000*/;



  ctr
    -1.0e6*i1*i2/(i3*i4)-x6+x7=-144279.32477276,
    -x6-x7-(0) >= - best_value - eps,
    -x6-x7-(0) <= - best_value + eps;



  solve * ;
end ;
-------------------------------------------------------------------



Solving this CSP by RealPaver gives me the following output :

-------------------------------------------------------------------
Box 0 [11340 ms] [width 8.3528e-09] [vol 0]
i1 = 16
i2 = 19
i3 = 43
i4 = 49
x6 ~ [0..8.352799341082573e-09]
x7 ~ [1.643428473966196..1.643428482318996]

Solving in 11340ms
1 solution(s)
379903 split(s)
29 box(es) created in memory
-------------------------------------------------------------------



I need an explanation... :(


Nicolas