scholarly journals Compact representation of the full Broyden class of quasi-Newton updates

2018 ◽  
Vol 25 (5) ◽  
pp. e2186 ◽  
Author(s):  
Omar DeGuchy ◽  
Jennifer B. Erway ◽  
Roummel F. Marcia
Keyword(s):  
Compact Representation ◽  
Broyden Class ◽  
Quasi Newton

scholarly journals Exact linesearch limited-memory quasi-Newton methods for minimizing a quadratic function

2021 ◽  
Author(s):  
David Ek ◽  
Anders Forsgren
Keyword(s):  
Optimization Problems ◽  
Linear Equations ◽  
Quadratic Function ◽  
Compact Representation ◽  
Test Collection ◽  
Newton Methods ◽  
Limited Memory ◽  
Broyden Class ◽  
Systems Of Linear Equations ◽  
Quasi Newton

AbstractThe main focus in this paper is exact linesearch methods for minimizing a quadratic function whose Hessian is positive definite. We give a class of limited-memory quasi-Newton Hessian approximations which generate search directions parallel to those of the BFGS method, or equivalently, to those of the method of preconditioned conjugate gradients. In the setting of reduced Hessians, the class provides a dynamical framework for the construction of limited-memory quasi-Newton methods. These methods attain finite termination on quadratic optimization problems in exact arithmetic. We show performance of the methods within this framework in finite precision arithmetic by numerical simulations on sequences of related systems of linear equations, which originate from the CUTEst test collection. In addition, we give a compact representation of the Hessian approximations in the full Broyden class for the general unconstrained optimization problem. This representation consists of explicit matrices and gradients only as vector components.

scholarly journals A Broyden Class of Quasi-Newton Methods for Riemannian Optimization

2015 ◽  
Vol 25 (3) ◽  
pp. 1660-1685 ◽  
Author(s):  
Wen Huang ◽  
K. A. Gallivan ◽  
P.-A. Absil
Keyword(s):  
Newton Methods ◽  
Riemannian Optimization ◽  
Broyden Class ◽  
Quasi Newton

scholarly journals Rates of superlinear convergence for classical quasi-Newton methods

2021 ◽  
Author(s):  
Anton Rodomanov ◽  
Yurii Nesterov
Keyword(s):  
Nonlinear Optimization ◽  
Superlinear Convergence ◽  
Local Convergence ◽  
Lipschitz Constant ◽  
Rates Of Convergence ◽  
Newton Methods ◽  
Long Time ◽  
Broyden Class ◽  
Quasi Newton ◽  
Convexity Parameter

AbstractWe study the local convergence of classical quasi-Newton methods for nonlinear optimization. Although it was well established a long time ago that asymptotically these methods converge superlinearly, the corresponding rates of convergence still remain unknown. In this paper, we address this problem. We obtain first explicit non-asymptotic rates of superlinear convergence for the standard quasi-Newton methods, which are based on the updating formulas from the convex Broyden class. In particular, for the well-known DFP and BFGS methods, we obtain the rates of the form $$(\frac{n L^2}{\mu ^2 k})^{k/2}$$ ( n L 2 μ 2 k ) k / 2 and $$(\frac{n L}{\mu k})^{k/2}$$ ( nL μ k ) k / 2 respectively, where k is the iteration counter, n is the dimension of the problem, $$\mu $$ μ is the strong convexity parameter, and L is the Lipschitz constant of the gradient.

Đánh giá hiệu quả của giải thuật Quasi-Newton trong điều khiển trượt thích nghi sử dụng mạng nơ-ron RBF

2018 ◽  
Vol 54(7) ◽  
pp. 27
Author(s):  
Phạm Thanh Tùng ◽  
Nguyễn Chí Ngôn ◽  
Lê Thị Kiều Mai ◽  
Nguyễn Đình Tứ ◽  
Đồng Văn Hướng ◽  
...  
Keyword(s):  
Quasi Newton

scholarly journals Robust Iterative Solvers for Gao Type Nonlinear Beam Models in Elasticity

2021 ◽  
Vol 0 (0) ◽  
Author(s):  
B. Borsos ◽  
János Karátson
Keyword(s):  
Finite Element ◽  
Newton Method ◽  
Newton's Method ◽  
Numerical Experiments ◽  
Elliptic Problems ◽  
Iterative Solvers ◽  
Finite Element Solution ◽  
Element Solution ◽  
Nonlinear Beam ◽  
Quasi Newton

Abstract The goal of this paper is to present various types of iterative solvers: gradient iteration, Newton’s method and a quasi-Newton method, for the finite element solution of elliptic problems arising in Gao type beam models (a geometrical type of nonlinearity, with respect to the Euler–Bernoulli hypothesis). Robust behaviour, i.e., convergence independently of the mesh parameters, is proved for these methods, and they are also tested with numerical experiments.

scholarly journals Method for designing multi-input system identification signals using a compact time-frequency representation

2021 ◽  
Author(s):  
Mathias Stefan Roeser ◽  
Nicolas Fezans
Keyword(s):  
System Identification ◽  
Design Method ◽  
Flight Test ◽  
Compact Representation ◽  
Time Frequency ◽  
Stability And Control ◽  
Frequency Representation ◽  
Aerodynamic Parameters ◽  
Definition Of ◽  
And Control

AbstractA flight test campaign for system identification is a costly and time-consuming task. Models derived from wind tunnel experiments and CFD calculations must be validated and/or updated with flight data to match the real aircraft stability and control characteristics. Classical maneuvers for system identification are mostly one-surface-at-a-time inputs and need to be performed several times at each flight condition. Various methods for defining very rich multi-axis maneuvers, for instance based on multisine/sum of sines signals, already exist. A new design method based on the wavelet transform allowing the definition of multi-axis inputs in the time-frequency domain has been developed. The compact representation chosen allows the user to define fairly complex maneuvers with very few parameters. This method is demonstrated using simulated flight test data from a high-quality Airbus A320 dynamic model. System identification is then performed with this data, and the results show that aerodynamic parameters can still be accurately estimated from these fairly simple multi-axis maneuvers.

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