This post is a sequel to the previous article on how to use the old Fortran code to solve optimization problems in C++ applications. This time we consider the L-BFGS-B algorithm for solving smooth and box-constrained optimization problems of the form $$ \begin{align*} \min_{x}\quad & f(x)\\ \text{subject to}\quad & l\le x\le u, \end{align*} $$ where $l$ and $u$ are simple bounds for $x\in\mathbb{R}^n$, and can take $-\infty$ and $+\infty$ values.

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L-BFGS is a well-known and widely-used optimization algorithm for smooth and unconstrained optimization problems. It was originally implemented in Fortran, and also has some more recent implementations including libLBFGS and my own LBFGS++. The Fortran code was written more than 30 years ago, and looks a bit exotic from today’s perspective. However, it is still one of the most stable and mature implementations of the L-BFGS algorithm, and is typically used as a baseline in testing and benchmarking.

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Yixuan Qiu

Statistics, Data, and Programming

Associate Professor