Publication record · 18.cifr/1995.byrd.lbfgsb

A Limited Memory Algorithm for Bound Constrained Optimization

v1.0.0

Richard H. Byrd (University of Colorado), Peihuang Lu (Northwestern University), Jorge Nocedal (Northwestern University), Ciyou Zhu (Northwestern University)

RAI18.cifr/1995.byrd.lbfgsb

SIAM Journal on Scientific Computing· 1995· doi:10.1137/0916069

We describe a limited memory algorithm for solving large nonlinear optimization problems subject to simple bounds on the variables. The method is based on the gradient projection method and uses a limited memory BFGS matrix to approximate the Hessian of the objective function. We show that the method is globally convergent. Numerical tests on problems with up to 10,000 variables illustrate the performance of the method.

bound constrained optimizationlimited memory BFGSlarge scale optimizationquasi-Newton methodsgradient projection

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Large-scale bound-constrained optimization was intractable with full quasi-Newton methods due to O(n^2) Hessian storage. L-BFGS-B provides an efficient method for problems with millions of variables and simple bound constraints, common in scientific computing and ML.

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L-BFGS-B extends limited-memory BFGS to box constraints via a generalized Cauchy point that identifies active constraints cheaply, followed by subspace minimization using the L-BFGS Hessian. This enables large-scale constrained optimization with O(mn) memory instead of O(n^2).

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