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Combining Synchronous Transit and Quasi-Newton Methods to Find Transition States
Israel Journal of Chemistry, 1993C. Peng, H. Schlegel
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Quasi-Newton Methods for Saddle Point Problems and Beyond
Neural Information Processing Systems, 2021This paper studies quasi-Newton methods for solving strongly-convex-strongly-concave saddle point problems (SPP). We propose greedy and random Broyden family updates for SPP, which have explicit local superlinear convergence rate of ${\mathcal O}\big ...
Chengchang Liu, Luo Luo
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2021
In Chap. 6, multidimensional optimization methods were considered in which the search for the minimizer is carried out by using a set of conjugate directions. An important feature of some of these methods (e.g., the Fletcher–Reeves and Powell’s methods) is that explicit expressions for the second derivatives of \(f(\mathbf{x})\) are not required ...
Andreas Antoniou, Wu-Sheng Lu
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In Chap. 6, multidimensional optimization methods were considered in which the search for the minimizer is carried out by using a set of conjugate directions. An important feature of some of these methods (e.g., the Fletcher–Reeves and Powell’s methods) is that explicit expressions for the second derivatives of \(f(\mathbf{x})\) are not required ...
Andreas Antoniou, Wu-Sheng Lu
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Adaptive sampling quasi-Newton methods for zeroth-order stochastic optimization
Mathematical Programming Computation, 2021We consider unconstrained stochastic optimization problems with no available gradient information. Such problems arise in settings from derivative-free simulation optimization to reinforcement learning. We propose an adaptive sampling quasi-Newton method
Raghu Bollapragada, Stefan M. Wild
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2008
In this chapter we take another approach toward the development of methods lying somewhere intermediate to steepest descent and Newton’s method. Again working under the assumption that evaluation and use of the Hessian matrix is impractical or costly, the idea underlying quasi-Newton methods is to use an approximation to the inverse Hessian in place of
David G. Luenberger, Yinyu Ye
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In this chapter we take another approach toward the development of methods lying somewhere intermediate to steepest descent and Newton’s method. Again working under the assumption that evaluation and use of the Hessian matrix is impractical or costly, the idea underlying quasi-Newton methods is to use an approximation to the inverse Hessian in place of
David G. Luenberger, Yinyu Ye
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Approximate quasi-Newton methods
Mathematical Programming, 1990Newton-like iterative methods for nonlinear equations on Banach spaces are considered. It is proved how the local convergence behaviour of the quasi-Newton method in the infinite dimensional setting is affected by the refinement strategy. Applications to boundary value problems and integral equations are included.
Kelley, C. T., Sachs, E. W.
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Quasi-Newton parallel geometry optimization methods
The Journal of Chemical Physics, 2010Algorithms for parallel unconstrained minimization of molecular systems are examined. The overall framework of minimization is the same except for the choice of directions for updating the quasi-Newton Hessian. Ideally these directions are chosen so the updated Hessian gives steps that are same as using the Newton method.
Steven K, Burger, Paul W, Ayers
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2019
The Quasi-Newton methods do not compute the Hessian of nonlinear functions. The Hessian is updated by analyzing successive gradient vectors instead. The Quasi-Newton algorithm was first proposed by William C. Davidon, a physicist while working at Argonne National Laboratory, United States in 1959.
Shashi Kant Mishra, Bhagwat Ram
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The Quasi-Newton methods do not compute the Hessian of nonlinear functions. The Hessian is updated by analyzing successive gradient vectors instead. The Quasi-Newton algorithm was first proposed by William C. Davidon, a physicist while working at Argonne National Laboratory, United States in 1959.
Shashi Kant Mishra, Bhagwat Ram
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A Survey of Quasi-Newton Equations and Quasi-Newton Methods for Optimization
Annals of Operations Research, 2001zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Xu, Chengxian, Zhang, Jianzhong
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