Monotone and nonmonotone trust-region-based algorithms for large scale unconstrained optimization problems

摘要: Two trust regions algorithms for unconstrained nonlinear optimization problems are presented: a monotone and nonmonotone one. Both of them solve the region subproblem by spectral projected gradient (SPG) method proposed Birgin, Martinez Raydan (in SIAM J. Optim. 10(4):1196---1211, 2000). SPG is algorithm solving large-scale convex-constrained problems. It combines classical with choice steplength line search strategy. The simplicity (only requires matrix-vector products, one projection per iteration) rapid convergence this scheme fits nicely globalization techniques based on philosophy, In trial step evaluated acceptance via rule which can be considered generalization well known fraction Cauchy decrease condition Grippo, Lampariello Lucidi Numer. Anal. 23:707---716, 1986). Convergence properties extensive numerical results presented. Our establish robustness efficiency new algorithms.