randn(‘seed’, 1);
T = 96; % 15 minute intervals in a 24 hour period
t = (1:T) ';
u = 2 * exp(-0.6 * cos((t+30) * pi/T) +0.05 * randn(T,1));
p = 0.1 * exp(-0.6 * cos((t+40) * pi/T) -0.7 * cos(t * 4 * pi/T)+0.01 * randn(T,1));

C = 2.5; D = 2.5;
%cvx_quiet(true);
cvx_begin
variables c(T,1) q(T,1);
minimize(p '* (u+c));
subject to
%q(1)==50
c >= -D; c <= C;
q >= 0; q <= 100;
sum( c )>=30;
sum( c )<=30.1;
q(2:T) == q(1:T-1) + c(1:T-1);
q(96,1)==100
u+c>0
cvx_end

hello everyone,

I have an minimization code and I would like to q(1)==50. If I remove starting point of q, code is working but initial point is around 70 and I cannot change it. Do you have any solution?

q(1) == 50 makes the problem infeasible as reported by solver/CVX.

Changing the objective to minimize(q(1))
results in optimal objective value of 67.4 for the few different random number instances I tried. Hence, that is the minimum value of q(1) for which your original problem is feasible. That value of 67.4 does depend on the collection of other constraints and input data values occurring in them.

The constraint sum(c)<=30.1 is preventing q(1) == 50 from being feasible, although I am not saying it is the only such constraint. I replaced 30.1 by a new variable w, made w the objective function, and included q(1) == 50. The following problem had optimal objective value 47.5, which shows that at least for that random problem instance, if the constraint sum( c )<=30.1 were changed to sum( c )<= 47.5, the problem would still be feasible even with q(1) == 50.

cvx_begin
variables c(T,1) q(T,1) w;
minimize(w);
subject to
q(1)==50
c >= -D; c <= C;
q >= 0; q <= 100;
sum( c )>=30;
sum( c )<=w;
q(2:T) == q(1:T-1) + c(1:T-1);
q(96,1)==100
u+c>0
cvx_end

There are many other modifications to your model and input data which would make q(1) == 50 feasible. Because it is your model, only you know what to do to improve the situation from your perspective.

In this case, I was trying to develop a EV charging case. q represents SoC and c represents battery capacity that is why I put limit between 30-30.1 which is the max. the capacity of the battery. I just trying to select the initial SoC of vehicles so I can optimize with different levels of demand. I am still trying to solve the problem but thank you for your help and for giving me another approach