1. A hybrid of adjustable trust-region and nonmonotone algorithms for unconstrained optimization.
- Author
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Amini, Keyvan and Ahookhosh, Masoud
- Subjects
- *
MONOTONIC functions , *ALGORITHMS , *MATHEMATICAL optimization , *STOCHASTIC convergence , *QUADRATIC equations , *MATHEMATICAL proofs - Abstract
Abstract: This study devotes to incorporating a nonmonotone strategy with an automatically adjusted trust-region radius to propose a more efficient hybrid of trust-region approaches for unconstrained optimization. The primary objective of the paper is to introduce a more relaxed trust-region approach based on a novel extension in trust-region ratio and radius. The next aim is to employ stronger nonmonotone strategies, i.e. bigger trust-region ratios, far from the optimizer and weaker nonmonotone strategies, i.e. smaller trust-region ratios, close to the optimizer. The global convergence to first-order stationary points as well as the local superlinear and quadratic convergence rates are also proved under some reasonable conditions. Some preliminary numerical results and comparisons are also reported. [Copyright &y& Elsevier]
- Published
- 2014
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