Implementing an Optimization problem using matlab - matlab

Question

I am trying to implement an Optimization problem using matlab
Where N=100 , M=(N-1/k) and L=50.
N=100;
L = 50;
for K= 101:1:1000
M = (N-1)/K;
R=#(x) -((1./x(2)).*(N- (x(1).*M)-((min ( N./(L.*x(2)), K)-x(1))*(max(0,N-(L.*x(2).*x(1)))))/(x(1)+(min ( N./(L.*x(2)), K)-x(2)))) - (max(0,N-(L.*K*x(2)))));
LB = [1 1];
b=1:min((ceil(N/L)), K) ;
UB = [min((ceil(N./L)), K) ((N./(L*b))) ];
options = optimoptions('fmincon','Algorithm','interior-point'); % run interior-point algorithm
[xopt, vopt] = fmincon(R,1,[],[],[],[],LB,UB,[],options);
v(K) = -vopt;
end
plot(101:1000,v,'v-','LineWidth',2);
xlabel('Number of Users (K)');
ylabel('Delivery Rate (R)');
The following error appears:
Warning: Length of lower bounds is > length(x); ignoring extra bounds.
> In checkbounds (line 27)
In fmincon (line 318)
In R1 (line 19)
Warning: Length of upper bounds is > length(x); ignoring extra bounds.
> In checkbounds (line 41)
In fmincon (line 318)
In R1 (line 19)
Index exceeds array bounds.
Error in
R1>#(x)-((1./x(2)).*(N-(x(1).*M)-((min(N./(L.*x(2)),K)-x(1))*(max(0,N-(L.*x(2).*x(1)))))/(x(1)+(min(N./(L.*x(2)),K)-x(2))))-(max(0,N-(L.*K*x(2)))))
Error in fmincon (line 546)
initVals.f = feval(funfcn{3},X,varargin{:});
Error in R1 (line 19)
[xopt, vopt] = fmincon(R,1,[],[],[],[],LB,UB,[],options);
Caused by:
Failure in initial objective function evaluation. FMINCON cannot continue.
The output graph should be the one shown here:
(the lower bound curve)

Answer 1

Couples of mistakes
First, the initial guess should be an 1D array of length 2, kindly
replace 1 by [1, 1]
Better initialize the variable v first , it will speed up your
computation
The most important is the upper bound of l, as you can see it
depends on s and it's in the denominator, consider it as non linear
constraint then set UB = [] You will need to include nonlcon into
fmincon
The code is as follow
N=100;
L = 50;
t = 101:1:1000;
le = length(t);
v = zeros(1, le);
for K= 100:1:1000
M = (N-1)/K;
R = #(x) -(1./(x(1))).*(N-x(1).*((N-1)./K)-((min(ceil(N./(L.*x(2))), K)).*...
max(N -L.*x(1).*x(2), 0))./((x(1) +(min(ceil(N./(L.*x(2))), K))))...
-(max(N - K.*L.*x(2), 0)));
LB = [1 1];
options = optimoptions('fmincon','Algorithm','interior-point');
[xopt, vopt] = fmincon(R,[1, 1],[],[],[],[],LB,[],...
#(x)nonlincon(x(1), x(2),N, L, K ),options);
v(K-101+1) = -vopt;
end
plot(101:1000,v,'v-','LineWidth',2);
xlabel('Number of Users (K)');
ylabel('Delivery Rate (R)');
function [c, ceq] = nonlincon(s, l,N, L, K )
c(1) = l -N./(L.*s);
c(2) = s - min((ceil(N./L)), K) ;
ceq = [];
end