Abstract: Monotonicity is often a fundamental assumption involved in the modeling of a number of real-world applications. From an optimization perspective, monotonicity is formulated as partial order constraints among the optimization variables, commonly known as isotone optimization. In this paper, we develop an efficient, provable convergent algorithm for solving isotone optimization problems. The proposed algorithm is general in the sense that it can handle any arbitrary isotonic constraints and a wide range of objective functions. We evaluate our algorithm and state-of-the-art methods with experiments involving both synthetic and real-world data. The experimental results demonstrate that our algorithm is more efficient by one to four orders of magnitude than the state-of-the-art methods.