Objective function increases but solver converges --- Why?

Hi All,

I am trying to solve a constrained optimization problem in fmincon

But I am not sure why the solver converges when the value of the objective function keeps increasing. In the problem I actually try to minimize the cost function.

First-order      Norm of
 Iter F-count            f(x)  Feasibility   optimality         step
    0      10    4.832863e+02    9.049e+00    4.227e-02
    1      21    1.102633e+03    4.064e+00    1.773e+03    4.846e+02
    2      31    3.135305e+03    6.418e-01    1.748e+04    3.303e+02
    3      41    3.838079e+03    1.503e-01    2.712e+04    1.434e+02
    4      51    5.643491e+03    1.751e-02    1.479e+04    1.056e+02
    5      64    1.104272e+04    2.133e-04    1.475e+04    4.097e+01
    6      78    1.114938e+04    3.426e-07    1.583e+00    2.615e-01
    7      89    1.114955e+04    3.189e-09    1.910e+01    4.891e-04
    8     104    1.114956e+04    1.458e-11    3.254e-01    3.897e-06
    9     119    1.114956e+04    1.779e-12    2.596e-01    3.332e-09
   10     134    1.114956e+04    2.554e-13    2.519e-01    3.315e-10
   11     149    1.114956e+04    4.795e-14    2.509e-01    8.456e-11

Local minimum possible. Constraints satisfied.

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

I have solved the same problem without constraints and the objective function decreases with iterations

 14     150    3.019962e+00    0.000e+00    2.483e-03    2.052e+03
   15     160    1.582527e+00    0.000e+00    1.598e-03    1.897e+03
   16     170    1.098656e+00    0.000e+00    1.042e-03    1.503e+03
   17     180    9.917733e-01    0.000e+00    7.543e-04    9.265e+02

Any help in understanding why the solver converges when objective function increases in constrained case will be useful.

Side note: MATLAB version 2020a. More details on the problem here

[Torsten]

Most probably you start with a point that is not feasible, but gives a lower value of the objective function than those in the feasible region.

[Deepa Maheshvare]

Ok, I think propably my constraints are changing the feasible space. I have used the same starting points for unconstrained problem.

Equation 1:

Equation 2:

I am trying to estimate in equation 2 and I am using equation 2 as constraints. (Is this wrong?)The objective function minimizes the error in time course results obtained from eqns 1 and 2. And I am using trapezoidal rule to write down the constraints

[Deepa Maheshvare]

Any suggestions?

Answer 1

[Pranav Verma]

Hi Deepa,

Please refer to the below discussions on the similar lines:

https://www.mathworks.com/matlabcentral/answers/577537-fmincon-does-not-converge-to-the-best-solution

https://www.mathworks.com/matlabcentral/answers/358500-fmincon-with-nonlcon-does-not-converge-to-optimum-value

Thanks