The problem is that I dont have a closed form expression for B_k in terms of μ_k. if I have a set of values for μ_k to get the corresponding B_k values I'll have to solve a system of 25 non-linear equations which can be done using MATLAB
Neither are required. Instead of solving the 25 equations, you just add Bk to the list of unknown variables in your problem. The 25 equations become equality constraints in B and mu and and the inequality constraint in your post becomes a linear inequality constraint on B only.