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Projected pseudotransient continuation. (English) Zbl 1180.65060

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.

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

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