How to solve the "Array indices must be positive integers or logical values" when using optimization toolbox? - matlab

Question

I am trying to implement this optimization problem through optimization toolbox:
where N = 60 files and K = 130 users when 1/K ≤ M ≤ t∗N/K, for which t∗ =3.
so I wrote this code:
clear all;
close all;
clc;
N=60;
t=3;
K=130;
for M=0:0.1:1.4
r=zeros(size(1:M));
f=le(1/K,M);
c=le(M,3*N/K);
if f || c
R2 = #(s) -(s-(s./ floor(N./s)).*M);
LB = 1;
UB = min(N, K);
options = optimoptions('fmincon','Algorithm','interior-point'); % run interior-point algorithm
[sopt, ropt] = fmincon(R2,1,[],[],[],[],LB,UB,[],options);
r(M) = -ropt;
end
end
plot(0:1.4,r(M),'r-','LineWidth',2);
xlabel('Cache Capacity (M)');
ylabel('Delivery Rate (R)');
However the output should be as shown in the graph the one of cut-set bound
The error is as follows:
Array indices must be positive integers or logical values.
Error in try (line 17)
r(M) = -ropt;

Answer 1

First define r outside of the for loop
r =zeros(size(0:0.1:1.4));
To index r inside the for loop you need integer, M is a float Number.
you can just define an additional index i
Also you don't need to specify r indices while plotting if you want
to plot the entire array, and remember to keep the abscissa as
0:0.1:1.4
The code is as follow
N=60;
t=3;
K=130;
i = 0;
r = zeros(size(0:0.1:1.4));
for M=0:0.1:1.4
i = i+1;
f=le(1/K,M);
c=le(M,3*N/K);
if f || c
R2 = #(s) -(s-(s./ floor(N./s)).*M);
LB = 1;
UB = min(N, K);
options = optimoptions('fmincon','Algorithm','interior-point'); % run interior-point algorithm
[sopt, ropt] = fmincon(R2,1,[],[],[],[],LB,UB,[],options);
r(i) = -ropt;
end
end
plot(0:0.1:1.4,r,'r-','LineWidth',2);
xlabel('Cache Capacity (M)');
ylabel('Delivery Rate (R)');
Alternatively you just can predefine all M elements as M = 0:0.1:1.4, then loop around using integer index, that can be used also in indexing r
The corresponding code is as follow
N=60;
t=3;
K=130;
M = 0:0.1:1.4;
r = zeros(size(M));
for i = 1:length(M)
f=le(1/K,M(i));
c=le(M(i),3*N/K);
if f || c
R2 = #(s) -(s-(s./ floor(N./s)).*M(i));
LB = 1;
UB = min(N, K);
options = optimoptions('fmincon','Algorithm','interior-point'); % run interior-point algorithm
[sopt, ropt] = fmincon(R2,1,[],[],[],[],LB,UB,[],options);
r(i) = -ropt;
end
end
plot(0:0.1:1.4,r,'r-','LineWidth',2);
xlabel('Cache Capacity (M)');
ylabel('Delivery Rate (R)');
Graph