The Compiler as a Decomposed Optimization System

This paper revisits the central claim of Bilar (2007) that the structure of executables is the product of anengineered optimization process. We introduce the Network Utility Maximization (NUM) framework anddemonstrate that modern compiler architectures can be formally mapped onto distinct decomposition strategiesfrom optimization theory. Specifically, we show that ahead-of-time (AOT) pass pipelines implement primaldecomposition, just-in-time (JIT) compilers with profile-guided optimization implement dual decomposition,speculative optimization implements penalty methods, and link-time optimization implements the alternatingdirection method of multipliers (ADMM). This reframes the compiler not as a monolithic optimizer, but as asystem of interlocked, resource-allocating subsystems. The formalism generates testable predictions, which wevalidate empirically in a companion paper. This work provides a mathematical foundation for the originalpaper’s core insight and suggests new directions for compiler design.