Efficient solver for solving given MINLP problem. (Preferably open source)

Question

I am trying to solve an IP optimization problem using DoCPLEX. Here (x_p, y_p) are co-ordinates of points, R is a positive constant and M is a very large positive number.

DECISION VARIABLES:
x_c[j], y_c[j]: Continuous variables
g[i,j]: Binary variables
z[j]: Binary variables

OBJECTIVE FUNCTION:
sum(z[j]) for all j

One set of CONSTRAINTS:
R - ((x_p[i]-x_c[j])**2 + (y_p[i] - y_c[j])**2)**0.5 <= M*g[i,j] for all i and j

I tried the following:

1. For g[i,j]=0, x_p=0 and y_p=0, we have following equation:

x_c^2 + y_c^2 >= R^2, which is non convex

2. Tried solving the above problem using docplex.mp.model and got the following error:

Error: Model has non-convex quadratic constraint, name='C1_00'

3. Tried solving the above problem using docplex.cp.model, assuming all decision variables can take only integer values

Problem is solvable, but even smaller sized problem involving ~210 binary variable was solved in 45 hours.

Suggest a solver that can solve above MINLP problems (Objective value is discrete and one set of constraints is non-linear) relatively faster. As I need to solver larger problem instances that may involve 10,000+ binary variables within reasonable computation time. Any suggestion will be helpful.