1963/06/01 by Hugh Everett · 1,269 citations
Engineering · Mathematics · Computer Science · #Advanced Control Systems Optimization #Advanced Optimization Algorithms Research #Optimization and Variational Analysis #Lagrange multiplier #Mathematical optimization #Simple (philosophy) #Differentiable function #Set (abstract data type) #Constraint algorithm #Multiplier (economics) #Mathematics #Function (biology) #Fraction (chemistry) #Computer science
paper · doi:10.1287/opre.11.3.399
published in Operations Research 11(3), 399-417 (Institute for Operations Research and the Management Sciences)
openalex publication_date 1963/06/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/04
The usefulness of Lagrange multipliers for optimization in the presence of constraints is not limited to differentiable functions. They can be applied to problems of maximizing an arbitrary real valued objective function over any set whatever, subject to bounds on the values of any other finite collection of real valued functions denned on the same set. While the use of the Lagrange multipliers does not guarantee that a solution will necessarily be found for all problems, it is “fail-safe” in the sense that any solution found by their use is a true solution. Since the method is so simple compared to other available methods it is often worth trying first, and succeeds in a surprising fraction of cases. They are particularly well suited to the solution of problems of allocating limited resources among a set of independent activities.