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Expertise matching, aiming to find the alignment between experts and queries, is a common problem in many real applications such as conference paper-reviewer assignment, product-reviewer alignment, and product-endorser matching. Most of existing methods for this problem usually find “relevant” experts for each query independently by using, e.g., an information retrieval method. However, in real-world systems, various domain-specific constraints must be considered. For example, to review a paper, it is desirable that there is at least one senior reviewer to guide the reviewing process. An important question is: “Can we design a framework to efficiently find the optimal solution for expertise matching under various constraints?” This paper explores such an approach by formulating the expertise matching problem in a constraint based optimization framework. Interestingly, the problem can be linked to a convex cost flow problem, which guarantees an optimal solution under given constraints. We also present an online matching algorithm to support incorporating user feedbacks in real time. The proposed approach has been evaluated on two different genres of expertise matching problems. Experimental results validate the effectiveness of the proposed approach.