Is this a DC Programming problem?I don’t know how to solve the nonconvex optimization problem by CVX.Can you give some advices?
Thank you very much！
No. The problem is nonconvex and hence cvx is not applicable.
As @Erling says.
The P_i and Q_i, individually, or when summed, are neither convex nor concave. Per my calculations in MAPLE, for at least some parameter values, the Hessian has both positive and negative eigenvalues, even for 0 \le x_i, and \sum{x_i } \le 1. If \sum{P_i} or \sum{Q_i} were both concave or both convex, then Difference of Convex Programming could be applied. But they are not, unless perhaps with suitable restriction of parameter values. And even then, there would be a matter of whether they could be expressed in CVX.
The best advice is to carefully read Why isn't CVX accepting my model? READ THIS FIRST! . Perhaps study “Convex Optimization” by Boyd and Vandenberghe https://web.stanford.edu/~boyd/cvxbook/ and work the exercises.
Thank you for your reply！
Your answer is very helpful to me, thank you for your reply.