Over-all sum value in fmincon for multiple x

Sir, i just want to know that how to write the over all sum <= 1-beta in the constraints?

e.g. if value of beta =0.4,

and i have 6 phi values to optimize, i have to optimize its value but the sum of all these 6 phi values not exceed 1-beta (i.e 0.6).

i will be thank full to you, if you could answer this question.

[Matt J]

Are you sure you only have 6 unknowns? In your earlier post, you had more.

https://www.mathworks.com/matlabcentral/answers/480223-how-to-write-series-of-multiple-non-linear-constraints-for-optimization-using-fmincon-in-matlab

[Maheen Fazal]

Sir i just gave a number, it differes according. depends on me that how many values i take.

Answer 1

[Matt J]

Are you sure you only have 6 unknowns? In your earlier post, you had more.

https://www.mathworks.com/matlabcentral/answers/480223-how-to-write-series-of-multiple-non-linear-constraints-for-optimization-using-fmincon-in-matlab

If you truly only have 6 unknowns, use the A,b inputs in

x = fmincon(fun,x0,A,b,______)

with

A=ones(1,6);
b=1-beta;

[Maheen Fazal]

can i take lower bounds and uper bounds of x from this same constraint?

[Matt J]

As discussed in your previous thread, it is posible but not recommended to use the A, b arguments to enforce simple bounds. Use the lb,ub input arguments for that:

x = fmincon(fun,x0,A,b,Aeq,beq,lb,ub,nonlcon,options)

[Maheen Fazal]

Thank you for your precious time.

Matt J i am still confused that the above constraint is used as what???

1) shall i use it as linear inequality constrain?

2) as lower and upper bounds?

3) or as both?

and you answered me that this is the way to write the linear inequality constraint as below:

A=ones(1,6);

b=1-beta;

i understood the method which you explained but i mentioned that summation of all the x values should be less than 1-B, here i didn't see any thing for the summation of all x values???

just answer me this question .thank you in advance

[Matt J]

i mentioned that summation of all the x values should be less than 1-B, here i didn't see any thing for the summation of all x values???

fmincon requires you to express linear (in)equality constraints using matrix-vector multiplication A*x<=b. Simple summation over x(i) can be expressed this way by taking A=ones(1,6). Example:

>> x=rand(6,1); A=ones(1,6);

>> A*x

ans =

    1.9809

>> sum(x)

ans =

    1.9809

Matt J i am still confused that the above constraint is used as what???

You have shown 3 different types of constraints:

This is a linear inequality constraint. As we have discussed, this is to be expressed using the A,b arguments

A=ones(1,6); b=1-beta;

These are also linear inequality constraints, but they are simple lower bounds, so you should specify them using the lb, ub arguments,

lb=zeros(6,1); ub=[];

If you had upper bounds as well, you would set ub to something more interesting.

You haven't told us what these look like, but if it they are similar to your previous thread, they are nonlinear constraints. You must write a nonlcon function for those. In this case, they should return a 6x1 vector c and and an empty 2nd argument ceq=[].

function [c,ceq]=constraints(x)  
c(1:6,1) = Rconstant-R(x);
ceq=[];
end

Putting it all together, your call to fmincon will look like this,

A=ones(1,6); b=1-beta;
lb=zeros(6,1); ub=[];

x=fmincon(@objective,x0,A,b,[],[],lb,ub,@constraints);

[Maheen Fazal]

Thank you Sir for your help.

Sir, How do you define non-linearity? i watched a video and in that video it is defined as

x*y+y+z<=0, or x^2+y<=0.

if two parameters are multiplied by each other or if the same parameters is muliplied by itself is considered as non-linear constraint.

shall i follow this rule or it is different from this defination?

[Matt J]

A constraint is nonlinear if it is not linear. A linear constraint is one that can be expressed with matrix-vector multiplication,

A*x<=b
Aeq*x=beq

[Maheen Fazal]

pleasure Sir.