Interior-point algorithm vs SQP algoritm

Hi, I am running an optimal design problem by using fmincon with sqp algorithm and interior-point algorithm. SQP algorithm was found the optimal and the exit message was (Local minimum found) while interior-point algorithm was given an exit flag (2) with exit message (Local minimum possible). So I used the optimum value which is given from SQP and re-run interior-point algorithm , but I still get tha same message (Local minimum possible). Why sqp was found the optimal wile interior-point algorithm did not? Thanks to all in advance.

Answer 1

[Alan Weiss]

Perhaps you are running into an inaccuracy due to using an interior-point method, or perhaps your problem has very high curvature or some other irregularity. It is hard to know based on the information you supplied.

Did you check the value that the interior-point algorithm gave? Was it unsatisfactory? Did you consult the documentation on Local Minimum Possible? It might give you some ideas about what is going on.

Good luck,

Alan Weiss

MATLAB mathematical toolbox documentation

[Muna Shehan]

Thank you for your response. Dear Sir 1) I rerun fmincon with a smaller (TolFun=-4) and fmincon with interior-point algorithm was given me "Local minimum found that satisfies the constraints.", while fmincon with SQP was given me "Local minimum possible. Constraints satisfied." with different objective value for the same data input (the results is shown below), is this reasonable and the proposed value of TolFun is it accurate enough. 2)I have a confusion about checking the optimum value that I get from interior-point algorithm with TolFun=-4 by using "Check Nearby Points" because the output from fmincon,x, in the problem is a vector of seven elements, and I am not sure about the delta value, increment or decrement value, that I should add or subtract from the output that used to check the new objective function . 3) I rerun starting at final point and I did get neither exitflag (1) nor (2), actually I get "No feasible solution found." Can you please interpret the fmincon output data behavior and why the big difference between the objective function when fmincon used interior-point algorithm and SQP algorithm? any idea can help, please Thanks in advance

Interior-point First-order Norm of Iter F-count f(x) Feasibility optimality step 0 1 1.267119e+002 8.249e+000 7.573e+002 1 2 9.455037e+001 6.315e+000 3.974e+003 2.653e+001 2 3 8.079296e+001 5.386e+000 6.179e+003 1.298e+001 3 4 5.834199e+001 3.707e+000 1.178e+004 2.289e+001 4 5 5.356883e+001 3.329e+000 1.292e+004 4.986e+000 5 6 4.863383e+001 2.918e+000 1.421e+004 5.409e+000 6 7 2.315582e+001 2.419e-001 2.146e+004 3.541e+001 7 8 1.922367e+001 5.531e-002 2.510e+004 7.018e+000 8 9 1.652829e+001 8.892e-004 2.683e+004 4.761e+000 9 10 1.616538e+001 7.628e-003 2.993e+004 2.088e+000 10 12 1.574222e+001 3.441e-003 3.491e+004 2.900e+000 11 16 1.557995e+001 1.141e-002 3.871e+004 2.239e+000 12 20 1.551844e+001 2.017e-002 4.293e+004 2.490e+000 13 24 1.557486e+001 3.004e-002 4.752e+004 2.789e+000 14 28 1.573355e+001 3.907e-002 5.202e+004 2.950e+000 15 32 1.597043e+001 4.763e-002 5.613e+004 3.059e+000 16 36 1.624597e+001 5.369e-002 5.952e+004 3.035e+000 17 40 1.653425e+001 5.491e-002 6.202e+004 2.925e+000 18 44 1.680591e+001 5.332e-002 6.360e+004 2.691e+000 19 46 1.623598e+001 6.386e-002 6.254e+004 4.629e+000 20 47 1.731452e+001 2.031e-002 6.420e+004 3.053e+000 21 48 1.743835e+001 1.663e-002 6.411e+004 1.504e+000 22 49 1.753599e+001 2.050e-002 6.349e+004 3.083e+000 23 53 1.754284e+001 2.141e-002 6.300e+004 1.890e+000 24 58 1.755710e+001 2.295e-002 6.248e+004 1.577e+000 25 62 1.764624e+001 2.902e-002 6.145e+004 2.612e+000 26 64 1.730761e+001 2.459e-002 5.757e+004 6.899e+000 27 65 1.725259e+001 1.371e-002 5.634e+004 9.723e-001 28 67 1.739285e+001 1.757e-002 5.439e+004 3.704e+000 29 68 1.709089e+001 1.630e-003 5.361e+004 1.107e+000 30 70 1.689795e+001 3.910e-003 5.214e+004 2.514e+000

                                            First-order      Norm of
 Iter F-count            f(x)  Feasibility   optimality         step
   31      72   1.673228e+001   5.134e-003   1.391e+004   2.509e+000
   32      74   1.663905e+001   5.796e-003   2.161e+004   2.714e+000
   33      76   1.669077e+001   4.075e-003   1.947e+004   2.208e+000
   34      78   1.686107e+001   3.313e-003   1.709e+004   2.066e+000
   35      80   1.711979e+001   3.118e-003   1.637e+004   1.830e+000
   36      82   1.745226e+001   2.712e-003   1.357e+004   1.657e+000
   37      84   1.780765e+001   1.861e-003   1.186e+004   1.408e+000
   38      86   1.811605e+001   8.373e-004   1.103e+004   1.085e+000
   39      88   1.833220e+001   2.629e-004   1.164e+004   7.627e-001
   40      90   1.847421e+001   9.214e-005   1.640e+004   5.617e-001
   41      92   1.858397e+001   6.522e-005   1.938e+004   5.205e-001
   42      94   1.868685e+001   9.598e-005   1.227e+004   5.935e-001
   43      96   1.879185e+001   1.758e-004   1.066e+004   7.100e-001
   44      98   1.889754e+001   2.661e-004   1.074e+004   7.827e-001
   45     100   1.900088e+001   2.984e-004   1.766e+004   7.824e-001
   46     102   1.910188e+001   2.788e-004   2.294e+004   7.395e-001
   47     104   1.920181e+001   2.373e-004   1.605e+004   6.773e-001
   48     106   1.930109e+001   1.881e-004   9.666e+003   6.062e-001
   49     108   1.939901e+001   1.452e-004   3.851e+003   5.345e-001
   50     110   1.949428e+001   1.115e-004   1.397e+003   4.681e-001
   51     112   1.958544e+001   8.493e-005   6.107e+003   4.092e-001
   52     114   1.967122e+001   6.331e-005   1.033e+004   3.580e-001
   53     116   1.975091e+001   4.592e-005   1.411e+004   3.150e-001
   54     118   1.982469e+001   3.284e-005   1.755e+004   2.809e-001
   55     120   1.989361e+001   2.432e-005   2.073e+004   2.564e-001
   56     122   1.995917e+001   1.897e-005   2.377e+004   2.409e-001
   57     124   2.002281e+001   1.594e-005   2.675e+004   2.324e-001
   58     126   2.008554e+001   1.441e-005   2.973e+004   2.279e-001
   59     128   2.014770e+001   1.363e-005   3.271e+004   2.242e-001
   60     130   2.020914e+001   1.304e-005   3.567e+004   2.193e-001

                                            First-order      Norm of
 Iter F-count            f(x)  Feasibility   optimality         step
   61     132   2.026951e+001   1.230e-005   3.859e+004   2.127e-001
   62     134   2.032859e+001   1.133e-005   4.146e+004   2.054e-001
   63     136   2.038643e+001   1.025e-005   4.426e+004   1.985e-001
   64     138   2.044324e+001   9.177e-006   4.703e+004   1.929e-001
   65     140   2.049919e+001   8.202e-006   4.977e+004   1.883e-001
   66     142   2.055409e+001   7.328e-006   5.247e+004   1.834e-001
   67     144   2.060718e+001   6.505e-006   5.511e+004   1.762e-001
   68     146   2.065701e+001   5.662e-006   5.761e+004   1.645e-001
   69     148   2.070174e+001   4.755e-006   5.988e+004   1.472e-001
   70     150   2.073966e+001   3.779e-006   6.181e+004   1.249e-001
   71     152   2.076983e+001   2.780e-006   6.338e+004   9.997e-002
   72     156   2.077587e+001   1.556e-006   6.369e+004   2.011e-002
   73     166   2.077452e+001   1.139e-007   4.386e+000   3.843e-004
   74     172   2.077322e+001   1.484e-009   4.614e-002   2.886e-003

Local minimum found that satisfies the constraints.

Optimization completed because the objective function is non-decreasing in feasible directions, to within the selected value of the function tolerance, and constraints are satisfied to within the default value of the constraint tolerance.

criteria details

Sequential Norm of First-order Iter F-count f(x) Feasibility Steplength step optimality 0 8 1.407909e+001 0.000e+000 1.109e+005 1 18 5.406556e+000 0.000e+000 4.900e-001 5.906e-002 4.677e+004 2 26 3.743085e+000 0.000e+000 1.000e+000 1.166e-001 9.258e+002 3 34 3.583608e+000 7.207e-005 1.000e+000 1.294e-001 9.683e+001 4 42 3.549702e+000 9.629e-006 1.000e+000 5.165e-002 3.716e+001 5 53 3.547533e+000 1.126e-005 3.430e-001 3.916e-002 9.312e+000 6 62 3.544379e+000 1.671e-005 7.000e-001 6.205e-002 6.666e+000 7 70 3.532007e+000 8.576e-006 1.000e+000 5.108e-002 1.486e+001 8 80 3.528891e+000 9.200e-006 4.900e-001 3.749e-002 1.648e+001 9 88 3.507190e+000 7.774e-007 1.000e+000 1.282e-002 6.769e+001 10 101 3.507148e+000 6.955e-007 1.681e-001 3.553e-003 5.343e+001 11 109 3.506259e+000 6.891e-008 1.000e+000 4.382e-003 1.351e+001 12 117 3.506177e+000 5.033e-008 1.000e+000 3.631e-003 1.577e+001 13 125 3.506039e+000 8.927e-009 1.000e+000 1.506e-003 3.148e+001 14 133 3.506011e+000 2.840e-010 1.000e+000 2.668e-004 6.886e+000 15 141 3.506011e+000 2.638e-010 1.000e+000 2.592e-004 4.220e+000 16 159 3.506011e+000 2.616e-010 2.825e-002 3.645e-005 4.212e+000 17 186 3.506011e+000 2.615e-010 1.140e-003 7.340e-006 4.212e+000 18 214 3.506011e+000 2.615e-010 4.600e-005 1.481e-006 4.212e+000

Local minimum possible. Constraints satisfied.`

fmincon stopped because the size of the current step is less than the default value of the step size tolerance and constraints are satisfied to within the default value of the constraint tolerance.

criteria details