Solving and Optimizing Large-Scale Nonlinear Systems

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Description

Non-monotone Barzilai-Borwein spectral methods for the solution and optimization of large-scale nonlinear systems.

Details

A tutorial style introduction to this package is available in a vignette, which can be viewed with vignette("BB").

The main functions in this package are:

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BBsolve A wrapper function to provide a robust stategy for solving large 
        systems of nonlinear equations. It calls dfsane with different 
	algorithm control settings, until a successfully converged solution
	is obtained.

BBoptim A wrapper function to provide a robust stategy for real valued function 
        optimization. It calls spg with different algorithm control settings, 
	until a successfully converged solution is obtained.

dfsane  function for solving large systems of nonlinear equations using a 
        derivative-free spectral approach 

sane	function for solving large systems of nonlinear equations using 
        spectral approach

spg	function for spectral projected gradient method for large-scale 
        optimization with simple constraints

Author(s)

Ravi Varadhan

References

J Barzilai, and JM Borwein (1988), Two-point step size gradient methods, IMA J Numerical Analysis, 8, 141-148.

Birgin EG, Martinez JM, and Raydan M (2000): Nonmonotone spectral projected gradient methods on convex sets, SIAM J Optimization, 10, 1196-1211.

Birgin EG, Martinez JM, and Raydan M (2001): SPG: software for convex-constrained optimization, ACM Transactions on Mathematical Software.

L Grippo, F Lampariello, and S Lucidi (1986), A nonmonotone line search technique for Newton's method, SIAM J on Numerical Analysis, 23, 707-716.

W LaCruz, and M Raydan (2003), Nonmonotone spectral methods for large-scale nonlinear systems, Optimization Methods and Software, 18, 583-599.

W LaCruz, JM Martinez, and M Raydan (2006), Spectral residual method without gradient information for solving large-scale nonlinear systems of equations, Mathematics of Computation, 75, 1429-1448.

M Raydan (1997), Barzilai-Borwein gradient method for large-scale unconstrained minimization problem, SIAM J of Optimization, 7, 26-33.

R Varadhan and C Roland (2008), Simple and globally-convergent methods for accelerating the convergence of any EM algorithm, Scandinavian J Statistics, doi: 10.1111/j.1467-9469.2007.00585.x.

R Varadhan and PD Gilbert (2009), BB: An R Package for Solving a Large System of Nonlinear Equations and for Optimizing a High-Dimensional Nonlinear Objective Function, J. Statistical Software, 32:4, http://www.jstatsoft.org/v32/i04/