Optimization for minimizing cylinder dimensions

Hi there, I am hoping to verify my optimization calculations using Matlab for a cylinder's dimensions (inner (x2) and outer (x1) radius) with 2 constraint equations (max bending and deflection).

The function (objfun.m) was inputed as:

function f=objfun (x)

f=(3667.81*x(1)^2)-(3667.81*x(2)^2);

end

The constraint (constraints.m) was inputed as:

function[c,ceq]=constraints(x)

c=[-30*10^6+(31.23*(x(1)^2-x(2)^2)^(-1))+(58.33*x(1)*(x(1)^4-x(2)^4)^(-1));-0.005+(6.23591*10^(-11)*(x(1)^4-x(2)^4)^(-1))];

ceq=[];

end

My optimum (Optimum.m) script is as follows:

clc

clear all

warning off

x0=[0,0];

f=objfun(x0);

[c,ceq]=constraints (x0);

options=optimset('LargeScale', 'off');

[x,fval]=fmincon(@objfun,x0,[],[],[],[],@constraints, options);

[c,ceq]=constraints (x);

But when it is run I end up with the following:

Error using fmincon (line 220)

FMINCON requires the following inputs to be of data type double: 'LB','UB'.

Error in Optimum (line 8)

[x,fval]=fmincon(@objfun,x0,[],[],[],[],@constraints, options);

Any insight and assistance would be greatly appreciated. I have also attempted to use the Optimization tool in Matlab with no results yet, so if anyone is comfortable with that App I would love to learn it. Thank you

Answer 1

[Alan Weiss]

You missed counting the fmincon input arguments. Try this instead:

[x,fval] = fmincon(@objfun,x0,[],[],[],[],[],[],@constraints,options);

Two hints to help in the future:

1. Try defining ALL the fmincon arguments, even the ones you don't use. Such as

A = [];
b = [];
Aeq = [];
beq = [];
lb = [];
ub = [];
[x,fval] = fmincon(@objfun,x0,A,b,Aeq,beq,lb,ub,@constraints,options);

2. Next time you want to ask a question and provide your code, use the {} Code button to make it look better (doesn't the code in my answer look better than that in your question?)

Alan Weiss

MATLAB mathematical toolbox documentation

[Sam Bergen]

Thank you so much for your response (and the tips!). I am still getting an error in that[x, fval] line.

Error using barrier (line 25)
Nonlinear constraint function is undefined at initial point. Fmincon cannot continue.

Error in fmincon (line 796)
    [X,FVAL,EXITFLAG,OUTPUT,LAMBDA,GRAD,HESSIAN] =
    barrier(funfcn,X,A,B,Aeq,Beq,l,u,confcn,options.HessFcn, ...

Error in Optimum (line 11)
[x,fval]=fmincon(@objfun,x0,[],[],[],[],[],[],@constraints, options);

If you have any ideas I'd greatly appreciate them. Thanks again!

[Torsten]

If x(1) and x(2) are both zero at the beginning, you divide by zero in the constraint function.

Choose a different initial guess for x.

Best wishes

Torsten.