Conjugate Gradient Optimization Algorithm
A Conjugate Gradient Optimization Algorithm is a batch function optimization algorithm that ...
- AKA: CG.
- See: L-BFGS Algorithm, Nonlinear Conjugate Gradient Algorithm, Biconjugate Gradient Algorithm.
References
2012
- http://en.wikipedia.org/wiki/Conjugate_gradient_method
- QUOTE: In mathematics, the conjugate gradient method is an algorithm for the numerical solution of particular systems of linear equations, namely those whose matrix is symmetric and positive-definite. The conjugate gradient method is an iterative method, so it can be applied to sparse systems that are too large to be handled by direct methods such as the Cholesky decomposition. Such systems often arise when numerically solving partial differential equations.
The conjugate gradient method can also be used to solve unconstrained optimization problems such as energy minimization. It was developed by Magnus Hestenes and Eduard Stiefel.[1]
The biconjugate gradient method provides a generalization to non-symmetric matrices. Various nonlinear conjugate gradient methods seek minima of nonlinear equations.
- QUOTE: In mathematics, the conjugate gradient method is an algorithm for the numerical solution of particular systems of linear equations, namely those whose matrix is symmetric and positive-definite. The conjugate gradient method is an iterative method, so it can be applied to sparse systems that are too large to be handled by direct methods such as the Cholesky decomposition. Such systems often arise when numerically solving partial differential equations.
- ↑ Straeter, T. A.. "On the Extension of the Davidon-Broyden Class of Rank One, Quasi-Newton Minimization Methods to an Infinite Dimensional Hilbert Space with Applications to Optimal Control Problems". NASA Technical Reports Server. NASA. http://hdl.handle.net/2060/19710026200. Retrieved 10 October 2011.