the initial point is local minima for fmincon.

I am trying to solve a minimization problem using fmincon but the solver doesn't perform any optimization and gice this message. I have tried with all possible values of the initial condition, but the answer remain same. Please help me.

Iter F-count f(x) Feasibility Steplength step optimality \\

    0      41        7.501427e-02   0.000e+00                           0.000e+00

Initial point is a local minimum that satisfies the constraints.

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

[Torsten]

The most probable explanation is that you return a constant value to fmincon from the objective function independent of the x-vector the solver supplies.

But we cannot tell for sure unless we see your code.

Best wishes

Torsten.

[Muhammad Zeeshan Babar]

The code is given below. where the cost function involves only the minimization of trace of P_est. The control horizon length is N = 30 and the simulations are performed for k=currentInstant=100 samples.

Please explain your above answer according to this code.

%%%%%%%Initial values for the control inputs %%%%%%%%%%%%%%%%%
  a = +25;
  b = -25;
  u0 = a + (b-a)*rand(1, MPC.horizon);

    %%%%%%%%%%%%%Bound on control inputs %%%%%%%%%%%%%%%%%
    minu = -50*ones(1, MPC.horizon);
    maxu = +50*ones(1, MPC.horizon);

    %%%%%%%%%%%%fmincon function %%%%%%%%%%%%%%%%%

      A = [];                   % linear inequalities A*x < B
      B = [];

      Aeq = [];                 % linear equalities Aeq*x = Beq
      Beq = [];

    nonlcon = [];               % nonlinear inequalties or equalties

     fun = @(u)costFunction(x, u, currentInstant, MPC,r_x1, para, P_est,alpha); %function handle
    [uopt(:,i), Jopt(i), exitfl(i), outp{i}] = fmincon(fun, u0, A, B, Aeq, Beq, minu, maxu, nonlcon, options);

[Torsten]

Without seeing "costFunction", nothing can be said.

Best wishes

Torsten.

Answer 1

[Sidafa]

It looks as though fmincon has converged from the output. The objective function, as pointed out from the previous answer, may be constant or is solved at the initial guess.

Answer 2

[Julie Kraus]

Fmincon only finds a local minimum, if your start point is at a local minimum in all feasible directions it has found a local minimum.

You may have better luck with the global search, it will choose a bunch of different start points, which can yield a better solution.