Kelley, C. T.; Liao, Li-Zhi; Qi, Liqun; Chu, Moody T.; Reese, J. P.; Winton, C. Projected pseudotransient continuation. (English) Zbl 1180.65060 SIAM J. Numer. Anal. 46, No. 6, 3071-3083 (2008). Summary: We propose and analyze a pseudotransient continuation algorithm for dynamics on subsets of \(\mathbb R^N\). Examples include certain flows on manifolds and the dynamic formulation of bound-constrained optimization problems. The method gets its global convergence properties from the dynamics and inherits its local convergence properties from any fast locally convergent iteration. Cited in 1 ReviewCited in 12 Documents MSC: 65H20 Global methods, including homotopy approaches to the numerical solution of nonlinear equations 65H10 Numerical computation of solutions to systems of equations 65K05 Numerical mathematical programming methods 65L05 Numerical methods for initial value problems involving ordinary differential equations 34A34 Nonlinear ordinary differential equations and systems 90C53 Methods of quasi-Newton type Keywords:pseudotransient continuation; constrained dynamics; gradient flow; bound-constrained optimization; quasi-Newton method; numerical examples; global convergence; local convergence Software:AUTO-86 PDFBibTeX XMLCite \textit{C. T. Kelley} et al., SIAM J. Numer. Anal. 46, No. 6, 3071--3083 (2008; Zbl 1180.65060) Full Text: DOI