Global convergence of a class of trust region algorithms for optimization with simple bounds
SIAM Journal on Numerical Analysis
A truncated Newton method with nonmonotone line search for unconstrained optimization
Journal of Optimization Theory and Applications
Family of projected descent methods for optimization problems with simple bounds
Journal of Optimization Theory and Applications
Trust-Region Interior-Point SQP Algorithms for a Class of Nonlinear Programming Problems
SIAM Journal on Control and Optimization
SIAM Journal on Control and Optimization
A Truncated Newton Algorithm for Large Scale Box Constrained Optimization
SIAM Journal on Optimization
Newton's Method for Large Bound-Constrained Optimization Problems
SIAM Journal on Optimization
Large-Scale Active-Set Box-Constrained Optimization Method with Spectral Projected Gradients
Computational Optimization and Applications
GALAHAD, a library of thread-safe Fortran 90 packages for large-scale nonlinear optimization
ACM Transactions on Mathematical Software (TOMS)
CUTEr and SifDec: A constrained and unconstrained testing environment, revisited
ACM Transactions on Mathematical Software (TOMS)
On Affine-Scaling Interior-Point Newton Methods for Nonlinear Minimization with Bound Constraints
Computational Optimization and Applications
A New Active Set Algorithm for Box Constrained Optimization
SIAM Journal on Optimization
Second-order negative-curvature methods for box-constrained and general constrained optimization
Computational Optimization and Applications
Evaluating bound-constrained minimization software
Computational Optimization and Applications
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We are concerned with the solution of the bound constrained minimization problem {minf(x), l驴x驴u}. For the solution of this problem we propose an active set method that combines ideas from projected and nonmonotone Newton-type methods. It is based on an iteration of the form x k+1=[x k +驴 k d k ]驴, where 驴 k is the steplength, d k is the search direction and [驴]驴 is the projection operator on the set [l,u]. At each iteration a new formula to estimate the active set is first employed. Then the components $d_{N}^{k}$ of d k corresponding to the free variables are determined by a truncated Newton method, and the components $d_{A}^{k}$ of d k corresponding to the active variables are computed by a Barzilai-Borwein gradient method. The steplength 驴 k is computed by an adaptation of the nonmonotone stabilization technique proposed in Grippo et al. (Numer. Math. 59:779---805, 1991). The method is a feasible one, since it maintains feasibility of the iterates x k , and is well suited for large-scale problems, since it uses matrix-vector products only in the truncated Newton method for computing $d_{N}^{k}$ . We prove the convergence of the method, with superlinear rate under usual additional assumptions. An extensive numerical experimentation performed on an algorithmic implementation shows that the algorithm compares favorably with other widely used codes for bound constrained problems.