How to write objective function with one single vector variable?

Hi.

I'm now working filter design. The objective function takes only one variable, which should be a vector (length around 15). Now I want to know how to write an objective function with only one single vector variable. Also I want to know which solver should I choose. I see that fmincon is a commonly used method but I don't know the format of the objective function for my case.

Here's my objective function:

all = norm((g_etau + g_dev_etau*x),inf);
first = all((g_sample_num*g_pass_area(1)):(g_sample_num*g_pass_area(2)),:);
second = g_lambada_p * (g_lr_pass + g_gradient_lr_pass * x);
third = g_lambada_s*(g_lr_stop + g_gradient_lr_stop*x);
output = norm(first,inf)+norm(second,inf)+norm(third,inf);

You can see that all the x inside are the variables and others are fixed value. How should I reformat this so I can use any solvers to solve this problem?

Answer 1

[Walter Roberson]

function output = objective(x, g_etau, g_dev_etau, g_sample_num, g_pass_area, g_lambada_p, g_lr_pass, g_gradient_lr_pass, g_lambada_s, g_lr_stop, g_gradient_lr_stop)

    all = norm((g_etau + g_dev_etau*x),inf);
    first = all((g_sample_num*g_pass_area(1)):(g_sample_num*g_pass_area(2)),:);
    second = g_lambada_p * (g_lr_pass + g_gradient_lr_pass * x);
    third = g_lambada_s*(g_lr_stop + g_gradient_lr_stop*x);
    output = norm(first,inf)+norm(second,inf)+norm(third,inf);
  end

Together with

g_etau = something;
g_dev_etau = something_else;
g_sample_num = a_third_thing;
g_pass_area = a_fourth_thing_which_is_a_vector_of_length_2;
g_lambada_p = a_fifth_thing;
g_lr_pass = a_sixth_thing;
g_gradient_lr_pass = a_seventh_thing;
g_lambada_s = an_eighth_thing;
g_lr_stop = a_nineth_thing;
g_gradient_lr_stop = a_tenth_thing;

x_length = randi([13 17]);    %(length around 15)
x_guess = rand(1, x_length);

A = []; b = [];      %linear constraints
Aeq = []; beq = [];  %equality constraints
lb = []; ub = [];    %lower and upper bound constraints
nonlcon = [];        %non-linear constraints
options = [];        %options

best_x = fmincon( @(x) objective(x, g_etau, g_dev_etau, g_sample_num, g_pass_area, g_lambada_p, g_lr_pass, g_gradient_lr_pass, g_lambada_s, g_lr_stop, g_gradient_lr_stop), x_guess, A, b, Aeq, beq, lb, ub, nonlcon, options);

[Gelei Deng]

Thank you so much! So this means that the fmincon can directly handle a vector varibale right?

[Walter Roberson]

Sure, no problem.

It can handle array variables too, but you have to know how it thinks about array variables if you are building linear constraints. (Which is to say, it reshapes them to a column)