We study a class of nonconvex optimization problems in which the feasible set is defined by the nonconvex \(\ell _{p}\) ball, and the objective function is continuously differentiable. To tackle such structured problems, we propose a novel hybrid algorithm that combines the Frank-Wolfe method with the gradient projection method. The Frank-Wolfe step is amenable to a closed-form solution, while the gradient projection step can be efficiently performed in a reduced subspace. We prove the global convergence of the proposed algorithm and establish a worst-case convergence rate of \(O(1/\sqrt{k})\) in terms of the optimality error under reasonable assumptions. Numerical experiments demonstrate the practicality and efficiency of our proposed algorithm compared with existing cutting-edge methods.
