A nonmonotone line search technique for Newton's method
SIAM Journal on Numerical Analysis
A truncated Newton method with nonmonotone line search for unconstrained optimization
Journal of Optimization Theory and Applications
SIAM Journal on Numerical Analysis
Nonmonotonic trust region algorithm
Journal of Optimization Theory and Applications
Non-monotone trust-region algorithms for nonlinear optimization subject to convex constraints
Mathematical Programming: Series A and B
Trust-region methods
Solving the Trust-Region Subproblem using the Lanczos Method
SIAM Journal on Optimization
Global Convergence of a Trust-Region SQP-Filter Algorithm for General Nonlinear Programming
SIAM Journal on Optimization
On the nonmonotone line search
Journal of Optimization Theory and Applications
CUTEr and SifDec: A constrained and unconstrained testing environment, revisited
ACM Transactions on Mathematical Software (TOMS)
A globally convergent primal-dual interior-point filter method for nonlinear programming
Mathematical Programming: Series A and B
A Multidimensional Filter Algorithm for Nonlinear Equations and Nonlinear Least-Squares
SIAM Journal on Optimization
Line Search Filter Methods for Nonlinear Programming: Motivation and Global Convergence
SIAM Journal on Optimization
A Filter-Trust-Region Method for Unconstrained Optimization
SIAM Journal on Optimization
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We present a new filter trust-region approach for solving unconstrained nonlinear optimization problems making use of the filter technique introduced by Fletcher and Leyffer to generate non-monotone iterations. We also use the concept of a multidimensional filter used by Gould et al. (SIAM J. Optim. 15(1):17---38, 2004) and introduce a new filter criterion showing good properties. Moreover, we introduce a new technique for reducing the size of the filter. For the algorithm, we present two different convergence analyses. First, we show that at least one of the limit points of the sequence of the iterates is first-order critical. Second, we prove the stronger property that all the limit points are first-order critical for a modified version of our algorithm. We also show that, under suitable conditions, all the limit points are second-order critical. Finally, we compare our algorithm with a natural trust-region algorithm and the filter trust-region algorithm of Gould et al. on the CUTEr unconstrained test problems Gould et al. in ACM Trans. Math. Softw. 29(4):373---394, 2003. Numerical results demonstrate the efficiency and robustness of our proposed algorithms.