[Ipopt] IPOPT derivative checker

[Atri Dutta]

Hi, 

I have started using IPOPT (3.10) recently and I have a question about the derivative checker in IPOPT. For the problem I am trying to solve, I used the derivative checker to validate the Jacobian and Hessian matrices I provided. I have provided exact expressions for the derivatives and the first-order and second-order derivative checkers yield no error. However, when I change the default value (which I believe is 10^-8) of relative value of perturbation to 10^-11 by setting options.ipopt.derivative_test_perturbation = 1e-11, the derivative checker yields 5 errors, e.g.  
   
* jac_g [   28,    1] = -1.8224453361523556e+00 v  ~ -1.8226593993855391e+00  [ 1.174e-04]
* jac_g [   31,    5] = -1.2191598536919732e+00 v  ~ -1.2192913345643319e+00  [ 1.078e-04]
* jac_g [   16,   47] =  6.3458246639357195e-04 v  ~  5.3290705182007514e-04  [ 1.017e-04]
* jac_g [   16,   48] = -1.4383040775181648e-04 v  ~ -2.6645352591003757e-04  [ 1.226e-04]
* jac_g [   16,   97] =  3.8229219906022398e-04 v  ~  2.6645352591003757e-04  [ 1.158e-04]

Note that options.ipopt.derivative_test_perturbation = 1e-10 yields no error, while options.ipopt.derivative_test_perturbation = 1e-12 drastically increases the number of errors in first-order derivatives to 170. I was wondering what this means, and if this can have any implication on solution of the problem I am trying to solve. 

Thanks, 
Atri. 

PS: Some details about the test problem for which I was checking the derivatives: 
Number of nonzeros in equality constraint Jacobian...:      521
Number of nonzeros in inequality constraint Jacobian.:        0
Number of nonzeros in Lagrangian Hessian.............:      198

Total number of variables............................:       91
                     variables with only lower bounds:        0
                variables with lower and upper bounds:       91
                     variables with only upper bounds:        0
Total number of equality constraints.................:       63
Total number of inequality constraints...............:        0
        inequality constraints with only lower bounds:        0
   inequality constraints with lower and upper bounds:        0
        inequality constraints with only upper bounds:        0