[Bonmin] is the problem in a non-differentiable objective function?

[Diogo Alagador]

Dear all,

I have a MINLP to solve and I am using the NEOS solvers facility, in  
order to reach the Bonmin solver.
My problem is in the prob.mod file (below),and data in the data.dat (below).
However some problems arose in the solving procedures (below).

Can you tell me if the problem is one of infeasibility of objective  
function differentiation, as written in one line of warnings, of if  
some other previous bugs exist?

Grateful in advance,
My best regards,

Diogo André
Évora, Portugal


#########################################################
#########################################################
#########################################################
# FILE prob.mod

param bbb;

param sss;
param ddd;
param length {i in 1..ddd};

param cls;
param cost {j in 1..cls};

param mat{i in 1..ddd, j in 1..cls};

set x1;
set x0;
set rep_sss;
param ttt {k in rep_sss};

var x{j in 1..cls} binary;


maximize OBJ:
	-sum{i in 1..ddd}(
		(sum{j in 1..cls} mat[i,j]*x[j]/sum{k in 1..sss} (sum{h in 1..cls}  
mat[k,h]*x[h]))*
		length[i]*
		log(sum{j in 1..cls} mat[i,j]*x[j]/sum{k in 1..sss} (sum{h in  
1..cls} mat[k,h]*x[h])));


subject to B:
	sum{j in 1..cls} cost[j]*x[j] = bbb;
subject to P {k in x1}:
	x[k]=1;
subject to U {k in x0}:
	x[k]=0;
subject to T {k in rep_sss}:
	sum{j in 1..cls} mat[k,j]*x[j] >= ttt[k];

#########################################################
#########################################################
#########################################################
# FILE data.dat

  param bbb :=  2 ;
  param sss :=  7 ;
  param ddd :=  12 ;
  param length :=
  1   1
  2   1
  3   2
  4   3
  5   2
  6   1
  7   1
  8   2
  9   1
  10   1
  11   1
  12   1;
  param cls := 9 ;
  param cost :=
  1   1
  2   1
  3   1
  4   1
  5   1
  6   1
  7   1
  8   1
  9   1;
  param mat: 1 2 3 4 5 6 7 8 9 :=
  1   1 0 0 0 1 0 0 0 0
  2   0 0 0 0 1 0 0 0 0
  3   1 1 0 1 0 0 1 0 0
  4   0 1 0 0 1 0 0 0 0
  5   0 0 1 0 0 0 0 0 0
  6   0 0 1 0 1 0 1 0 0
  7   0 1 1 0 0 0 0 0 0
  8   2 1 0 1 2 0 1 0 0
  9   0 2 3 0 2 0 1 0 0
  10   0 1 3 0 1 0 1 0 0
  11   0 1 2 0 1 0 1 0 0
  12   1 0 0 0 2 0 0 0 0;
  set x1 :=  ;
  set x0 := 6 8 9 ;
  set rep_sss := 1 3 ;
  param ttt :=
  1   1
  3   1;

#########################################################
#########################################################
#########################################################
# ON SCREEN WARNINGS IN NEOS BONMIN SOLVER


Executing /opt/neos/Drivers/bonmin-ampl/bonmin-ampl-driver.py at time:  
2012-02-19 11:32:59.242536
File exists
You are using the solver bonmin-ampl.
Executing AMPL.
processing data.
processing commands.

Presolve eliminates 3 constraints and 3 variables.
Adjusted problem:
6 variables, all nonlinear
3 constraints, all linear; 12 nonzeros
	1 equality constraint
	2 inequality constraints
1 nonlinear objective; 6 nonzeros.

Error: ERROR WHILE EVALUATING GRAD_F in  
OsiTMINLPInterface::getObjCoefficients()
Bonmin 1.5.1 using Cbc 2.7.2 and Ipopt 3.10.1
bonmin:

Error: Ipopt exited with error code -13 Invalid number detected
******************************************************************************
Error: Error at _cmdno 3 executing "solve" command
This program contains Ipopt, a library for large-scale nonlinear optimization.
Error: (file amplin, line 95, offset 1421):
  Ipopt is released as open source code under the Eclipse Public License (EPL).
Error:
          For more information visit http://projects.coin-or.org/Ipopt
Error: 	Error differentiating OBJ: division by 0
******************************************************************************

NLP0012I
               Num      Status      Obj             It       time       
            Location
NLP0014I             1         OPT -5.13612945.5g       13 0.004999g
NLP0012I
               Num      Status      Obj             It       time       
            Location
NLP0014I             1         OPT -5.13485915.5g        7 0.002g
Error in an AMPL evaluation. Run with "halt_on_ampl_error yes" to see details.
NLP0014I             2         OPT -4.87686515.5g       17 0.005999g
NLP0014I             3         OPT -4.86155255.5g       15 0.004g
Error in an AMPL evaluation. Run with "halt_on_ampl_error yes" to see details.
NLP0014I             4         OPT 5.5093683e-3165.5g        0 0g
Error in an AMPL evaluation. Run with "halt_on_ampl_error yes" to see details.
Error in an AMPL evaluation. Run with "halt_on_ampl_error yes" to see details.
NLP0012I
               Num      Status      Obj             It       time       
            Location
NLP0014I             1         OPT 6.9532934e-3105.5g        0 0g
Error in an AMPL evaluation. Run with "halt_on_ampl_error yes" to see details.
Error in an AMPL evaluation. Run with "halt_on_ampl_error yes" to see details.
NLP0014I             2         OPT 5.5082118e-3165.5g        0 0g
Cbc0012I Integer solution of 6.9532934e-310 found by DiveMIPFractional  
after 0 iterations and 0 nodes (0.01 seconds)
NLP0014I             2         OPT -5.03528325.5g        7 0.001g
NLP0014I             3         OPT -4.87686525.5g       13 0.004999g
Error in an AMPL evaluation. Run with "halt_on_ampl_error yes" to see details.
Error in an AMPL evaluation. Run with "halt_on_ampl_error yes" to see details.

  	"Aborted"

bonmin: Error encountered in optimization.
  Error (512) in /opt/ampl/ampl -R amplin