LMBOPT: a limited memory method for bound-constrained optimization

• Published in: Mathematical programming computation Vol. 14; no. 2; pp. 271 - 318
• Main Authors: Kimiaei, Morteza, Neumaier, Arnold, Azmi, Behzad
• Format: Journal Article
• Language: English
• Published: Berlin/Heidelberg Springer Berlin Heidelberg 01.06.2022; Springer Nature B.V
• Subjects: Algorithms; Full Length Paper; Mathematics; Mathematics and Statistics; Mathematics of Computing; Operations Research/Decision Theory; Optimization; Searching; Solvers; Theory of Computation; Limited memory technique; Primary 90C30; Exact gradient; 65K05; Bound constrained optimization; 90C06; Robust line search method
• ISSN: 1867-2949; 1867-2957; 1867-2957
• DOI: 10.1007/s12532-021-00213-x

Recently, Neumaier and Azmi gave a comprehensive convergence theory for a generic algorithm for bound constrained optimization problems with a continuously differentiable objective function. The algorithm combines an active set strategy with a gradient-free line search CLS along a piecewise linear search path defined by directions chosen to reduce zigzagging. This paper describes LMBOPT, an efficient implementation of this scheme. It employs new limited memory techniques for computing the search directions, improves CLS by adding various safeguards relevant when finite precision arithmetic is used, and adds many practical enhancements in other details. The paper compares LMBOPT and several other solvers on the unconstrained and bound constrained problems from the CUTEst collection and makes recommendations on which solver to use and when. Depending on the problem class, the problem dimension, and the precise goal, the best solvers are LMBOPT, ASACG, and LMBFG-EIG-MS.