We introduce KLAP, a novel passivation method for linear time-invariant (LTI) systems, based on the low-rank factorized formulation of the Kalman-Yakubovich-Popov (KYP) lemma. In this framework, the passivation problem corresponds to finding a perturbation to a given non-passive system that renders the system passive while minimizing the H2 distance. Unlike traditional methods that rely on linear matrix inequality (LMI) constraints, our approach reformulates the problem as an unconstrained optimization problem whose objective function can be differentiated efficiently even in large-scale settings. We prove that all global minimizers of this problem yield the same passive system. Moreover, in the absence of a feedthrough term, every local minimizer is also global. When a non-trivial feedthrough term is present, we examine the connection between global minimizers and extremal solutions of algebraic Riccati equations, which offer insight into identifying local minima. To enhance numerical performance, we propose an initialization strategy that modifies the feedthrough term and incorporate a restart mechanism when it is likely that the optimization has converged to a local minimum. The effectiveness of KLAP is demonstrated through numerical experiments.