Recently, the latticized linear programming problems subjected to max-min and max-product fuzzy relational inequalities (FRI) have been studied extensively and have been utilized in many interesting applications. In this paper, we introduce a new generalization of the latticized optimization problems whose objective is a non-linear function defined by an arbitrary continuous s-norm (t-conorm), and whose constraints are formed as an FRI defined by an arbitrary continuous t-norm. Firstly, the feasible region of the problem is completely characterized and two necessary and sufficient conditions are proposed to determine the feasibility of the problem. Also, a general method is proposed for finding the exact optimal solutions of the non-linear model. Then, in order to accelerate the general method, five simplification techniques are provided that reduce the work of computing an optimal solution. Additionally, a polynomial-time method is presented for solving general latticized linear optimization problems subjected to the continuous FRI. These special cases of the primal problem give some extensions of the result in Yang. Et. al., where the latticized linear programming subjected to max-product FRI is considered. Moreover, an application of the proposed non-linear model is described where the objective function and the FRI are defined by the well-known Lukasiewicz s-norm and product t-norm, respectively. Finally, a numerical example is provided to illustrate the proposed algorithm.