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Augmented Lagrangian and Operator-Splitting Methods in Nonlinear Mechanics
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In this article, an augmented Lagrangian method for the solution of variational problems is proposed. But this method is not suitable for continuous media and their mathematical modeling, such as viscoplasticity and elastoviscasticity.Abstract:
1. Some continuous media and their mathematical modeling 2. Variational formulations of the mechanical problems 3. Augmented Lagrangian methods for the solution of variational problems 4. Viscoplasticity and elastoviscoplasticity in small strains 5. Limit load analysis 6. Two-dimensional flow of incompressible viscoplastic fluids 7. Finite elasticity 8. Large displacement calculations of flexible rods References Index.read more
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Variationally consistent discretization schemes and numerical algorithms for contact problems
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Stochastic Quasi-Fejér Block-Coordinate Fixed Point Iterations with Random Sweeping
TL;DR: In this paper, the authors proposed block-coordinate fixed point algorithms with applications to nonlinear analysis and optimization in Hilbert spaces, based on a notion of stochastic quasi-Fejer monotonicity.
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Fixed-point iterations for asymptotically nonexpansive mappings in Banach spaces
Benlong Xu,Muhammad Aslam Noor +1 more
TL;DR: In this article, a three-step iterative scheme for asymptotically nonexpansive mappings in Banach spaces is proposed and analyzed, which includes Ishikawa-type and Mann-type interations as special cases.
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Alternating direction methods for classical and ptychographic phase retrieval
TL;DR: It is shown how the augmented Lagrangian alternating direction method can be used to solve both the classical and ptychographic phase retrieval problems, and its performance against standard algorithms for phase retrieval on a number of test images is compared.
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