Implements a sophisticated expression template system that allows users to build complex objective functions from simpler components (e.g., f = g + 2*h) while automatically computing gradients and Hessians. Demonstrates advanced C++ template metaprogramming skills by handling different differentiability modes and enabling natural mathematical syntax for function composition. The system is largely self-contained and could be extracted for use in other mathematical libraries with minimal adaptation.

Provides a robust implementation of the Augmented Lagrangian method for constrained optimization that handles both equality and inequality constraints. Features include automatic penalty scaling, warm-up strategies for early iterations, KKT-based stopping criteria, and best iterate tracking to handle non-convex objectives. The Powell-Hestenes-Rockafellar formulation for inequalities prevents unboundedness issues. While it depends on supporting components, the core algorithm is well-encapsulated and could be reused with different inner solvers.

Implements the Hager-Zhang (2006) line search algorithm, a sophisticated method that satisfies Wolfe conditions for optimization. The code includes detailed comments referencing the original research paper and appears to be a faithful implementation. This component is highly self-contained, depending only on basic function types, and could be easily extracted for use in other optimization frameworks. It demonstrates correct implementation of a non-trivial numerical algorithm.