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
Numerical recipes in C (2nd ed.): the art of scientific computing
Numerical recipes in C (2nd ed.): the art of scientific computing
Interior Proximal and Multiplier Methods Based on Second Order Homogeneous Kernels
Mathematics of Operations Research
Algorithm 813: SPG—Software for Convex-Constrained Optimization
ACM Transactions on Mathematical Software (TOMS)
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
SIAM Journal on Optimization
Rescaling and Stepsize Selection in Proximal Methods Using Separable Generalized Distances
SIAM Journal on Optimization
The Ordered Subsets Mirror Descent Optimization Method with Applications to Tomography
SIAM Journal on Optimization
CUTEr and SifDec: A constrained and unconstrained testing environment, revisited
ACM Transactions on Mathematical Software (TOMS)
Interior Gradient and Epsilon-Subgradient Descent Methods for Constrained Convex Minimization
Mathematics of Operations Research
A Nonmonotone Line Search Technique and Its Application to Unconstrained Optimization
SIAM Journal on Optimization
Interior projection-like methods for monotone variational inequalities
Mathematical Programming: Series A and B
Interior Gradient and Proximal Methods for Convex and Conic Optimization
SIAM Journal on Optimization
Mirror descent and nonlinear projected subgradient methods for convex optimization
Operations Research Letters
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We consider nonmonotone projected gradient methods based on non-Euclidean distances, which play the role of barrier for a given constraint set. Our basic scheme uses the resulting projection-like maps that produces interior trajectories, and combines it with the recent nonmonotone line search technique originally proposed for unconstrained problems by Zhang and Hager. The combination of these two ideas leads to produce a nonmonotone scheme for constrained nonconvex problems, which is proven to converge to a stationary point. Some variants of this algorithm that incorporate spectral steplength are also studied and compared with classical nonmonotone schemes based on the usual Euclidean projection. To validate our approach, we report on numerical results solving bound constrained problems from the CUTEr library collection.