Is it possible to add variables to my nonlinear constraints if they are not in the objective function?

I am using fmincon to minimize for my objective function:

objective = @(x) x(1)^2+x(2)^2;

But in my nonlinear constraints, I have three more variables: x(3), x(4) and x(5). I have four equations for coordinates (dependent on x(1),x(2),x(3),x(4) and x(5)), for which I think x(3), x(4) and x(5) can be calculated from. But as you can guess, I am not able to solve for my model so far. These are my nonlinear constraints:

function [c,ceq] = nlcon34(x)
%x=[wxo,wyo,vxo,vyo,vzo]
%x(1)=wxo x(2)=wyo x(3)=vxo x(4)=vyo x(5)=vzo 
%x(6)=t, is nu (-vzo*ez +/- sqrt((vzo*ez)^2-2*g*Zg))/-g, kies de -, dan
%t= (vzo*ez + sqrt((vzo*ez)^2-2*g*Zg))/g

a       = 0.83; % ball factor
R       = 0.1155; %radius ball
g       = 9.81; %gravity
ez      = 0.84; % COR
LAT     = 1.5; %hoogte locatie bovenlat (weet niet precies nog)
L       = 0.75/2; %width goal, from middle
xbounce = 0.7; %place where ball bounces first, with respect to x-as from mid
ybounce = 9; % waar bal stuitert tov y-as vanaf midden. y=0 op middenstip. y=7.4 m op penaltystip. y=11 m op doellijn

zg = (0:0.1:(LAT-R)); % Is this possible?
t  = (x(5)*ez+sqrt((x(5)*ez)^2-(2*g*zg)))./g; % Dots in right place?
xg = (x(3)+(a*R*x(2)))*t./(1+a) + 2*x(5)*x(3)/g;
yg = (x(4)+(a*R*x(1)))*t./(1+a) + 2*x(5)*x(4)/g;

xb = 2*x(5)*x(3)/g;
yb = 2*x(5)*x(4)/g;

vabs = sqrt(x(3)^2+x(4)^2+x(5)^2);
phi  = atan2(x(5),sqrt(x(3)^2+x(4)^2));

c(1)   = xg - L;         %xg < L
c(2)   = -(xg+L);        %-L < xg
c(3)   = vabs-12;        % v < 12
c(4)   = -vabs;          % v > 0. Is this necessary? If no imaginary numbers it will always be positive I guess
c(5)   = phi - pi/2;     % phi < pi/2
c(6)   = -phi;           % phi > 0
c(7)   = -t;             % t > 0

ceq(1) = yg - 11 - 7.4;      % yg = 11 m from middle, robot at 3.6 m from goal
ceq(2) = yb - ybounce - 7.4; % yb = ybounce from mid, robot at 3.6 m from goal, yb=ybounce-7.4 from robot
ceq(3) = xb - xbounce;       % bounce location in x, xb = xbounce (assuming robot on same x-line)
pause(1)
end

And with the script below I calculate fmincon. This results in a great deal of errors. I'm new to using fmincon, so there might be some obvious things that I'm missing. I was wondering if one of the problems might be that I cannot solve for x(3), x(4) and x(5) because they are not in the objective function? I have checked the "

How do I pass additional parameters to the constraint and objective functions in the Optimization Toolbox functions'

file, but I'm still not sure. I am now using some nonlinear constraints, for which some not even contain x(1) and x(2), is this possible? If not, how else can I solve for those constraints?

clear all;close all; clc

objective = @(x) x(1)^2+x(2)^2;

% initial guess (just random for now)
x0 = [20,20];

%you might see that these values are also already mentioned in the nonlinear constraints function. I'm not sure where they should be.
a       = 0.83; % ball factor
R       = 0.1155; %radius bal
g       = 9.81; %gravity
ez      = 0.84; % COR
LAT     = 1.5; %height
L       = 0.75/2; %width half goal
xbounce = 0.7; %place where ball bounces first, with respect to x-as from mid
ybounce = 9; %  waar bal stuitert tov y-as vanaf midden. y=0 op middenstip. y=7.4 m op penaltystip. y=11 m op doellijn

% variable bounds
lb = [];
ub = [];

% show initial objective
disp(['Initial Objective: ' num2str(objective(x0))])

% linear constraints
A = [];
b = [];
Aeq = [];
beq = [];

% nonlinear constraints
nonlincon = @nlcon34;

% optimize with fmincon
%[X,FVAL,EXITFLAG,OUTPUT,LAMBDA,GRAD,HESSIAN]
% = fmincon(FUN,X0,A,B,Aeq,Beq,LB,UB,NONLCON,OPTIONS)
options = optimoptions('fmincon', 'Algorithm','sqp', 'MaxIterations', 500000,'ConstraintTolerance', 1e-5, 'OptimalityTolerance', 1e-6, 'StepTolerance', 1e-12, 'MaxFunctionEvaluations', 5000);
x = fmincon(objective,x0,A,b,Aeq,beq,lb,ub,nonlincon,options);

% show final objective
disp(['Final Objective: ' num2str(objective(x))])

% print solution
disp('Solution')
disp(['wxo = ' num2str(x(1))])
disp(['wyo = ' num2str(x(2))])

Any help is welcome. Thanks in advance!

[Matt J]

And with the script below I calculate fmincon. This results in a great deal of errors.

It's usually a good idea to copy/paste the errors for us, so we know what they are.

Answer 1

[Matt J]

Your initial guess x0=[20,20] contains only 2 elements but it should contain 5 because that is how many unknowns you have. If you make your x0 of length N, then fmincon will know your problem has N unknowns and will pass vectors of length N to the objective and the constraints as it does its iterative search. However, this does not mean that within the code for your objective or constraints you must use all N of the x(i).

[Isabelle]

Okay thank you Matt! When I change x0 to

x0 = [20,20,10,10,10];

for example, my errors are as follows:

Initial Objective: 800
Unable to perform assignment because the indices on the left side are not compatible with the size of the right side.

Error in nlcon34 (line 27)
c(1)   = xg - L;         %xg < L

Error in fmincon (line 649)
        [ctmp,ceqtmp] = feval(confcn{3},X,varargin{:});

Error in fmincon_zaterdag28nov (line 38)
x = fmincon(objective,x0,A,b,Aeq,beq,lb,ub,nonlincon,options);

Caused by:
    Failure in initial nonlinear constraint function evaluation. FMINCON cannot continue.

[Matt J]

xg-L is a vector.

K>> xg-L

ans =

   31.1647   31.0867   31.0075   30.9271   30.8455   30.7626   30.6784   30.5927   30.5056   30.4168   30.3265   30.2343   30.1403   30.0443

You cannot put a vector into a scalar location c(1).

[Isabelle]

This solves my problem, thank you Matt!!

[Isabelle]

Hi Matt, I see that fmincon is ignoring my inequality constraints c(5) and c(6), might it be that there are no solutions for the constraining interval of phi, or is there a different problem? Changing the algorithm from 'sqp' to 'interior-point' does give an answer within the constraints of phi, but it now gives the error 'coverged to an infeasible point', and it changed the values of xb,yb,xg,yg,zg which I give as an input.