matlab fmincon _ nonlinear optimization

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jisoo jung
jisoo jung 2019-10-14
评论： jisoo jung 2019-10-14
Hi. I have been trying to resolve the following issues, but i cannot solve that.
Used thing : Nonlinear optimization
Used option is
options = optimoptions('fmincon',...
'StepTolerance',1e-10,'Hessian','lbfgs','Display','iter','Algorithm','sqp','Display','iter', 'MaxFunEvals',1e4,'MaxIter',1e4,'FiniteDifferenceType','central',...
'OptimalityTolerance',1e-6)
My question is
  1. the objection function value is not changed after certain time.
2. But the first order optimality isnot zero.
3. The lase thing is that (the exitflag = 2) is not good solution ? ( optimality is not zero )
Please check the fig as following.
In my objective function is unknown function. I just known input variable & output. becuase I am using the linearization mode.
So I can only use difference in gradient.
I try to all of thing that i can do, but i cannot solve the problem. Please give me good solution.
( I also using 'interior-point', 'sqp' etc).
Thanks for reading.
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Bruno Luong
Bruno Luong 2019-10-14
编辑：Bruno Luong 2019-10-14
"You mean first optimality have to be considered both case?"
Yes. Condider this simple 2D example, where I minimize a x(1) on the circle x(1)^2+x(2)^2 = 1 using non-linear constraint:
[x,fval,exitflag,output] = fmincon(@fun,[0; 0],[],[],[],[],[],[],@mycon)
function f=fun(x)
f = x(1);
end
function [c,ceq]=mycon(x)
c = [];
ceq = sum(x.^2)-1;
end
The output of FMINCON is
output =
struct with fields:
iterations: 9
funcCount: 43
constrviolation: 5.1070e-14
stepsize: 2.1720e-07
algorithm: 'interior-point'
firstorderopt: 2.2352e-08
cgiterations: 4
message: '↵Local minimum found that satisfies the constraints.↵↵Optimization completed because the objective function is non-decreasing in ↵feasible directions, to within the value of the optimality tolerance,↵and constraints are satisfied to within the value of the constraint tolerance.↵↵<stopping criteria details>↵↵Optimization completed: The relative first-order optimality measure, 2.235174e-08,↵is less than options.OptimalityTolerance = 1.000000e-06, and the relative maximum constraint↵violation, 5.107026e-14, is less than options.ConstraintTolerance = 1.000000e-06.↵↵'
The first order reach 2.2352e-08 and trigger the stop of FMINCON (read the message) because the firstorder is rightly computed from the gradient of the Lagrangian.
jisoo jung
jisoo jung 2019-10-14
So , waht do you think aobut my phnomenom ?
The fval is converge. and also constraint also converge to some value.
;But the optimality is very large.
What is your opnion ? and I want to resolve this prob. Please.
My function is unknown function . So I cannot use gradinet personally.
Please give your help.

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