I have a max-min problem with some non-convex constraints, that I convert to approximate convex ones.

max min X_i

s.t.

convex_const

non_convex_const

I am trying to use the Successive convex approximation (SCA) after converting the non_convex_const to a new approximated convex constraint ( new_convex_const).

to handle the max-min objective, I am using an auxiliary variable as an objective and used the bisection method to find the solution of the the new convex problem in each iteration of the SCA

max t

s.t.

convex_const

new_convex_const

x_i>=t , i =1-to-N

I formulated the problem using CVX assuming two loops , one for the SCA and one inner loop for the bisection search.

The problem now that i always get infeasible solution for the inner loop

My question: is the infeasibility due to wrong idea of merging both bisection and SCA or due to infeasible initialization of the first iteration of the SCA

Thank you in advance