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Attribute-based pricing---giving a price to potential product attributes individually and allowing customers to choose the attributes that form the final product---has been shown to improve customer satisfaction in the hospitality industry. In this paper, we consider the problem of finding optimal attribute prices to maximize the expected revenue from selling to a customer who chooses one product from a set of products that differ by only a few attributes. Because of complicated substitution effects among the final products that share common attributes, expected revenue is not concave in attribute prices. Nonetheless, we provide an algorithm to solve the attribute pricing problem and show that it converges to a stationary point that provides a high-quality solution to the problem. Through numerical experiments, we show our algorithm is, on average, ten times faster than gradient-based methods, both in terms of runtime and number of iterations. We also extend our algorithm to a setting where attribute prices are constrained through linear inequalities and prove convergence to a stationary point. We implement our algorithm on a real hotel data set and demonstrate its revenue benefits.