Rosenbrock methods

Rosenbrock methods refers to either of two distinct ideas in numerical computation, both named for Howard H. Rosenbrock.

Numerical solution of differential equations

Rosenbrock methods for stiff differential equations are a family of multistep methods for solving ordinary differential equations that contain a wide range of characteristic timescales.^[1][2] They are related to the implicit Runge-Kutta methods^[3] and are also known as Kaps-Rentrop methods.^[4]

Search method

Rosenbrock search is a numerical optimization algorithm applicable to optimization problems in which the objective function is inexpensive to compute and the derivative either does not exist or cannot be computed efficiently.^[5] The idea of Rosenbrock search is also used to initialize some root-finding routines, such as fzero (based on Brent's method) in Matlab. Rosenbrock search is a form of derivate-free search but may perform better on functions with sharp ridges.^[6] The method often identifies such a ridge which, in many applications, leads to a solution.^[7]

See also

• Rosenbrock function
• Adaptive coordinate descent

References

External links

• http://www.applied-mathematics.net/optimization/rosenbrock.html

Optimization: Algorithms, methods, and heuristics   Unconstrained nonlinear: Methods calling … … functions Golden section search Interpolation methods Line search Nelder–Mead method Successive parabolic interpolation … and gradients Convergence Trust region Wolfe conditions Quasi–Newton BFGS and L-BFGS DFP Symmetric rank-one (SR1) Other methods Gauss–Newton Gradient Levenberg–Marquardt Conjugate gradient … and Hessians Newton's method   Constrained nonlinear General Barrier methods Penalty methods Differentiable Augmented Lagrangian methods Sequential quadratic programming Successive linear programming   Convex optimization Convex minimization Cutting-plane method Reduced gradient (Frank–Wolfe) Subgradient method Linear and quadratic Interior point Ellipsoid algorithm of Khachiyan Projective algorithm of Karmarkar Basis-Exchange Simplex algorithm of Dantzig Revised simplex algorithm Criss-cross algorithm Principal pivoting algorithm of Lemke   Combinatorial Paradigms Approximation algorithm Dynamic programming Greedy algorithm Integer programming Branch & bound or cut Graph algorithms Minimum spanning tree Bellman–Ford Borůvka Dijkstra Floyd–Warshall Johnson Kruskal Network flows Dinic Edmonds–Karp Ford–Fulkerson Push-relabel maximum flow   Metaheuristics Evolutionary algorithm Hill climbing Local search Simulated annealing Tabu search Categories Algorithms and methods Heuristics Software