Compiler optimization is important to software performance, and modern processor architectures make optimization even more critical. However, many modern software applications use libraries providing high levels of abstraction. Such libraries often hinder effective optimization—the libraries are difficult to analyze using current compiler technology. For example, high-level libraries often use dynamic memory allocation and indirectly expressed control structures, such as iterator-based loops. Programs using these libraries often cannot achieve an optimal level of performance. On the other hand, software libraries have also been recognized as potentially aiding in program optimization. One proposed implementation of library-based optimization is to allow the library author, or a library user, to define custom analyses and optimizations. Only limited systems have been created to take advantage of this potential, however. One problem in creating a framework for defining new optimizations and analyses is how users are to specify them: implementing them by hand inside a compiler is difficult and prone to errors. Thus, a domain-specific language for library-based compiler optimizations would be beneficial. Many optimization specification languages have appeared in the literature, but they tend to be either limited in power or unnecessarily difficult to use. Therefore, I have designed, implemented, and evaluated the Pavilion language for specifying program analyses and optimizations, designed for library authors and users. These analyses and optimizations can be based on the implementation of a particular library, its use in a specific program, or on the properties of a broad range of types, expressed through concepts. The new system is intended to provide a high level of expressiveness, even though the intended users are unlikely to be compiler experts.