Hi, I am struggling to construct a code that solves a convex problem.
The problem is a maximization problem with an objective function which is continuous, smooth, and concave, but piecewised.
The problem is as follows:
In the above problem, B is a given constant, and C_i for all i are also given constants.
g_{i,1}(x), g_{i,2}(x), g_{i,3}(x) are all concavely increasing function with respect to x.
Also at x=C_i, g_{i,2} and g_{i,3} have the same values and the same derivatives, i.e., g_{i,2}(C_i)=g_{i,3}(C_i) and g_{i,2}’(C_i)=g_{i,3}’(C_i).
How can I solve this convex problem using CVX?
You cannot do that for an arbitrary function f. Therefore, you must have an explicit definition of the g functions.
Also
https://docs.mosek.com/modeling-cookbook/practical.html?highlight=piece#convex-univariate-piecewise-defined-functions
might be useful.
Actually functions, g, are explicitly given for me. So, I made a code with them, but the condition (xi>Ci) makes an error. Thank you for link, I will read it.
What I know for sure is that strict greater than is not possible.
Also I doubt you can formulate a function branches. You should be able to do with and that is why I made a reference to Mosek modelling cook book.
Finally showing you Cvx code might be useful because we have no clue what you did.
My code that causes the error is as follows:
Uset = func1(...); % given
Wset = func2(...); % given
Hset = func3(...); % given
cvx_precision best
cvx_begin quiet
variable x(N) nonnegative
sumF = 0;
for i = 1:N
u1 = Uset1(i); u2 = Uset2(i);
w1 = Wset1(i); w2 = Wset2(i);
h1 = Hset1(i); h2 = Hset2(i);
if w2/w1 <= h1/h2
sumF = sumF + log(1+h1*x(i));
elseif x(i) >= (w1/h2-w2/h1) / (w2-w1)
sumF = sumF + w2*log(1+h2*x(i));
else
sumF = sumF + w1*log(1+h1*cvxp(k))...
+ w1*log((w2-w1)/(h1-h2)*h2/w1)...
+ w2*log((h1-h2)/(w2-w1)*w2/h1);
end
end
maximize sumF
subject to
sum(x) <= 50
cvx_end
Then, I have an error message as follows:
Disciplined convex programming error:
Constraints may not appear in if/then statements.
I guess that the error occurs because elseif ~~~~~ phrase.
So, I am thinking how to fix it.
You can’t just express your function using if-else where the if-else conditions include values of optimization variables. You would have to model it carefully using binary variables as in the link you got from @Erling or some variation of that. There are resources on mixed-integer modeling of piecewise defined functions online.
