Interior-point algorithm vs SQP algoritm

2015 7 6
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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.

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Alan Weiss
Alan Weiss 2015-7-8

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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

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Muna Shehan
Muna Shehan 2015-7-8
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

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