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A non-negative latent factor analysis (NLFA)-based recommender can make precise recommendations by correctly representing the non-negative characteristic of industrial data. It commonly relies on a nonconvex and bilinear optimization process, where the effects of first-order solvers maybe significantly reduced. Higher order solvers like a Newton-type method are expected to make a breakthrough; however, its computation efficiency and scalability are greatly limited due to the numerous parameters involved in a Hessian matrix. To address this issue, this article proposes an approach for assimilating second-order information for building NLFA-based recommenders. The key idea is an inner second-order solver that employs a Hessian-free method for avoiding the highly expensive manipulations of a Hessian matrix. Empirical studies on eight data cases emerging from real industrial applications indicate that the proposed approach outperforms state-of-the-art models in prediction accuracy with affordable computational burden. [ABSTRACT FROM AUTHOR]