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In this paper, we present a new trust region method for unconstrained nonlinear programming in which we blend adaptive trust region algorithm by non-monotone strategy to propose a new non-monotone trust region algorithm with automatically... more
In this paper, we present a new trust region method for unconstrained nonlinear programming in which we blend adaptive trust region algorithm by non-monotone strategy to propose a new non-monotone trust region algorithm with automatically adjusted radius. Both non-monotone strategy and adaptive technique can help us introduce a new algorithm that reduces the number of iterations and function evaluations. The
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This study is concerned with some algorithms for solving high-dimensional convex optimization problems appearing in applied sciences like signal and image processing, machine learning and statistics. We improve an optimal �rst-order... more
This study is concerned with some algorithms for solving high-dimensional convex optimization problems appearing in applied sciences like signal and image processing, machine learning and statistics. We improve an optimal �rst-order approach for a class of objective functions including costly a�ne terms by employing a special multidimensional subspace search. We report some numerical results for some imaging problems including nonsmooth regularization terms.
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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... more
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.