Although I don't understand your problem setup because the variables in the objective function are not influenced by your constraint, here is a running code:
%Parameters of the system%
Fk = 10^10;
Bk = 20*10^6;
p = 0.1; %Watts
g0 = 10^(-4);
w0 = -100;
v = 0.2*10^(-11); %J/cycle
C = 8*500; %cycles/bit
fe = 100*10^9; %Hz
fc = 500*10^9; %Hz
s_enc = 240*10^6; %cycles, random number
s_dec = 240*10^6; %cycles, random number
w = 0.5; %decision weight
%Parameters of the system that change%
fl = (0.4:0.1:1)*10^9; %Hz
D = linspace(0,10,100)*10^6; %MB
theta = randi([0,1]);
r = randi([1 length(fl)],1,1); %generate random nuber
fl_temp = fl(r);
q = randi([1 length(D)],1,1); %generate random nuber
D_temp = D(r);
%variables of the system%
w0_watt = 10^(w0/10)/1000;
R = Bk*log2(1+(p*g0^2)/(w0_watt*Bk));
% E_enc = v*s_enc*D_temp*a3;
% t_end_dec = (v*s_enc*D_temp/fc)*a3 + (v*s_dec*D_temp/fe)*a3;
% E_l = v*C*D_temp*a1;
% T_l = (C*D_temp/fl_temp)*a1;
% T_s = (C*D_temp/fe)*a2;
% T_c = (C*D_temp/fc)*a3;
% T_trans = D_temp/R*(a2 + a3);
% E_r = p*T_trans;
% E_sec = theta*(E_enc + E_r) + (1-theta)*E_r;
% T_sec = theta*(t_end_dec + T_trans) + (1-theta)*T_trans;
%
% E = E_l + E_sec;
% T = max([T_l, T_sec + T_s, T_sec + T_c]);
%Soving the problem%
%set initial guess values for the problem variables%
a1 = 1/3;
a2 = 1/3;
a3 = 1/3;
Emax = 1.0;
Tmax = 1.0;
%Load guess values into an array%
x0 = [a1 a2 a3 Emax Tmax];
E_enc = v*s_enc*D_temp*a3;
t_end_dec = (v*s_enc*D_temp/fc)*a3 + (v*s_dec*D_temp/fe)*a3;
E_l = v*C*D_temp*a1;
T_l = (C*D_temp/fl_temp)*a1;
T_s = (C*D_temp/fe)*a2;
T_c = (C*D_temp/fc)*a3;
T_trans = D_temp/R*(a2 + a3);
E_r = p*T_trans;
E_sec = theta*(E_enc + E_r) + (1-theta)*E_r;
T_sec = theta*(t_end_dec + T_trans) + (1-theta)*T_trans;
E = E_l + E_sec;
T = max([T_l, T_sec + T_s, T_sec + T_c]);
%set lower and upper bounds%
lb = [0 0 0 E T];
ub = [1.0 1.0 1.0 1000.0 1000.0];
%call solver to minimize the objective function given the constraints%
% fmincon(fun,x0,A,b,Aeq,beq,lb,ub,nonlcon)%
A = [1 1 1 0 0];
b = 1.0;
Aeq = [];
beq = [];
[x,fval] = fmincon(@(x)objective(x,w),x0,A,b,Aeq,beq,lb,ub)
end
%define objective function for optimization%
function obj = objective(x,w)
Emax = x(4);
Tmax = x(5);
obj = w*Emax + (1-w)*Tmax;
end
