A nonmonotone line search technique for Newton's method
SIAM Journal on Numerical Analysis
Nonmonotonic trust region algorithm
Journal of Optimization Theory and Applications
Molecular conformations from distance matrices
Journal of Computational Chemistry
Non-monotone trust-region algorithms for nonlinear optimization subject to convex constraints
Mathematical Programming: Series A and B
Testing Unconstrained Optimization Software
ACM Transactions on Mathematical Software (TOMS)
Trust-region methods
Algorithm 813: SPG—Software for Convex-Constrained Optimization
ACM Transactions on Mathematical Software (TOMS)
A D. C. Optimization Algorithm for Solving the Trust-Region Subproblem
SIAM Journal on Optimization
The Barzilai and Borwein Gradient Method for the Large Scale Unconstrained Minimization Problem
SIAM Journal on Optimization
Nonmonotone Spectral Projected Gradient Methods on Convex Sets
SIAM Journal on Optimization
Journal of Computational and Applied Mathematics
An efficient nonmonotone trust-region method for unconstrained optimization
Numerical Algorithms
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Two trust regions algorithms for unconstrained nonlinear optimization problems are presented: a monotone and a nonmonotone one. Both of them solve the trust region subproblem by the spectral projected gradient (SPG) method proposed by Birgin, Martínez and Raydan (in SIAM J. Optim. 10(4):1196---1211, 2000). SPG is a nonmonotone projected gradient algorithm for solving large-scale convex-constrained optimization problems. It combines the classical projected gradient method with the spectral gradient choice of steplength and a nonmonotone line search strategy. The simplicity (only requires matrix-vector products, and one projection per iteration) and rapid convergence of this scheme fits nicely with globalization techniques based on the trust region philosophy, for large-scale problems. In the nonmonotone algorithm the trial step is evaluated by acceptance via a rule which can be considered a generalization of the well known fraction of Cauchy decrease condition and a generalization of the nonmonotone line search proposed by Grippo, Lampariello and Lucidi (in SIAM J. Numer. Anal. 23:707---716, 1986). Convergence properties and extensive numerical results are presented. Our results establish the robustness and efficiency of the new algorithms.