Lewis, Robert Michael; Torczon, Virginia Pattern search algorithms for bound constrained minimization. (English) Zbl 1031.90047 SIAM J. Optim. 9, No. 4, 1082-1099 (1999). The authors extend pattern search algorithms to bound constrained minimization of the form \[ \begin{aligned}\text{minimize }\quad & f(x)\\ \text{subject to }\quad & 1\leq x\leq u. \end{aligned} \] A general class of feasible point pattern search algorithms is developed and the global convergence to a Karush-Kuhn-Tucker-point is proved. Reviewer: H.Benker (Merseburg) Cited in 2 ReviewsCited in 70 Documents MSC: 90C30 Nonlinear programming 65K05 Numerical mathematical programming methods Keywords:bound constrained optimization; convergence analysis; pattern search methods; direct search methods; globalization strategies; alternating variable search; axial relaxation; local variation; coordinate search; evolutionary operation; multidirectional search PDFBibTeX XMLCite \textit{R. M. Lewis} and \textit{V. Torczon}, SIAM J. Optim. 9, No. 4, 1082--1099 (1999; Zbl 1031.90047) Full Text: DOI