In this paper, we investigate the problem of minimizing p-th order controversy within a network, assuming a framework of opinion evolution based on the well-established Friedkin-Johnsen (FJ) model. We define p-th order controversy as \(f_p(L) = s^T (I + L)^{-p} s\) , where s represents the vector of users’ fixed albeit undisclosed initial opinions, I is the identity matrix, and L is the graph Laplacian associated with the underlying network. Notably, for the case of \(p=1\) , this function transforms into the widely recognized polarization-disagreement index, and for \(p=2\) , it aligns with the standard polarization [1, 2]. We focus on minimizing \(f_p(L)\) within a novel and realistic framework, where users’ initial opinions s are undisclosed. Due to the undisclosed nature of users’ initial opinions, achieving the exact minimization of \(f_p(L)\) proves unattainable within our innovative and practical framework. To address this challenge, we introduce a novel semidefinite programming formulation designed to enable the minimization of the upper bound of \(f_p(L)\) without the need for knowledge of initial opinions. Furthermore, our empirical findings demonstrate its effectiveness, surpassing current state-of-the-art methodologies.