A New Family Of Globally Convergent Conjugate Gradient Methods

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A derivative-free projection method for solving convex

the proposed method is globally convergent under mild assumptions. Preliminary numerical results show that the proposed method works quite well for large-scale problems. Most recently, based on the projection technique4, the spectral gradient method5 and the classical PRP conjugate gradient method8, Liu9 proposed a derivative-free spectral

Life Science Journal 2013;10(2) http://www.lifesciencesite

corresponding system of equations, other methods like natural gradient is linearly convergent, while Newton method is quadratically convergent [26,27]. Amari [3] derived a Newton-based method for optimization of a single ICA model in his stability analysis of the ICA problem. Taking the derivative of (4), we find, Hessian matrix are evaluated as

Metric Representations of Data via the Kernel-based Sammon

Conjugate Gradient or quasi-Newton methods, which are economical in storage demands and, simultaneously, offer reasonable convergent speeds. Nevertheless, a fast algorithm for SM learning, that has gained significant popularity, is iterative majorization (IM) in the guise of the SMACOF algorithm [9]. IM generates a convergent sequence of simpler

Optimization: Applications, Algorithms, and Computation

Optimization: Applications, Algorithms, and Computation 24 Lectures on Nonlinear Optimization and Beyond Sven Leyffer (with help from Pietro Belotti, Christian Kirches, Jeff Linderoth, Jim Luedtke, and Ashutosh Mahajan)

Global convergence of Riemannian line search methods with a

9 In addition, we develop a new globally convergent Riemannian conjugate gradient method that 10 satis es the direction assumptions introduced in this work. Finally, some numerical experiments are 11 performed in order to demonstrate the e ectiveness of the new procedure. 12 Key words.

In Memoriam

[30]W. Zhou, J. D. Gri n, and I. G. Akrotirianakis. A globally convergent modi ed conjugate-gradient line-search algorithm with inertia controlling. Technical Report 2009-01, 2009. [31]J. Martens. Deep learning via Hessian-free optimization. In Pro-ceedings of the 27th International Conference on Machine Learn-ing (ICML-10), pages 735{742, 2010.

A Two-Step Spectral Gradient Projection Method for System of

May 26, 2020 two-dimensional strictly convex quadratic functions. Recently, Dai et al. [6] proposed a family of gradient methods whose stepsize is a convex combination of tBB1 k and t BB2 k. The stepsize is obtained by solving the following problem Yx(t) = kx[(1/t)s k 1 y k 1]+(1 x)[s k 1 ty k 1]k 2. (9) It was shown that if 0 x 1 and hy k 1, s k 1i> 0

Unconstrained nonlinear optimization: Amoeba BFGS Linear

Family of nonlinear algorithms Amoeba (Nelder-Mead) method Solves nonlinear optimization pproblem roblem directly Requires no derivatives or line search Adapts its step size based on change in function value Conjugate gradient and quasi-Newton methods Require function, first derivatives* and line search

pmoptitext.pdf, page 1-442 @ Normalize - Wiley Online Library

Byrd, R. H. (1984). On the convergence of constrained optimization methods with accurate Hessian information on a subspace, Univ. of Colorado at Boulder, Dept. of Compo Sci. Report CU-CS-270-84. Byrd, R. H. and Shultz, G. A. (1982). A practical class of globally convergent active set

A Modified Nonlinear Conjugate Gradient Method for

regarded as very efficient conjugate gradient methods in and the two-parameter family in [25] as its subfamilies. The Global Convergence for the New

Room 3, Faculty of Natural Science Building, Redeemer s

Efficient Family of PRP and HS Hybrid Conjugate Gradient Methods for Unconstrained Optimization, Statistics, Optimization and Information Computing. (In Press). 4. Ezugwu, A.E., Adeleke, O. J., Akinyelu A.A. and Viriri S. (2019). Conceptual and numerical comparison of several metaheuristic algorithms on continuous

A Conjugate Gradient Algorithm with Sufficient Descent

The method (5)-(8) is a method that belongs to the family of scaled conjugate gradient methods introduced by Birgin and Martínez [3]. Observe that if f is a quadratic function and αk is selected to achieve the exact minimum of f in the direction , then and the formula (7) for dk sgk T k+1 =0 βk a reduces to the Dai and Yuan computational

P rehled Publika cn cinnosti - cs.cas.cz

34. Lukˇsan L.: Numerical methods for unconstrained optimization. Technical Report DMSIA 97/12, Universita degli Studi di Bergamo, 1997. 35. Lukˇsan L., Vlˇcek J.: Computational Experience with Globally Convergent Descent Methods for Large Sparse Systems of Nonlinear Equations. Optimization Methods and Software, Vol. 8, 1998, pp.201-223.

Globally convergence of nonlinear conjugate gradient method

GLOBALLY CONVERGENCE OF NONLINEAR CONJUGATE GRADIENT METHOD FOR UNCONSTRAINED OPTIMIZATION B. Sellami1,M.Belloufi1 and Y. Chaib1 Abstract. The conjugate gradient method is a useful and powerful approach for solving large-scale minimization problems. In this paper, a new nonlinear conjugate gradient method is proposed for large-

Seminal papers in nonlinear optimization

Conjugate gradient methods for large problems Generalizations of Conjugate Gradient methods for non-quadratic minimization were originally proposed by R. Fletcher and C. M. Reeves, Function minimization by conjugate gradients , Computer J. (1964) 149:154, and E. Polak and G. Ribi ere, Note sur la convergence de m ethodes de directions con-

pmoptipre.pdf, page 1-14 @ Normalize - Wiley Online Library

Chapter 3 Newton-like Methods. 3.1 Newton's Method 3.2 Quasi-Newton Methods. 3.3 Invariance, Metrics and Variational Properties 3.4 The Broyden Family 3.5 Numerical Experiments 3.6 Other Formulae. Questions for Chapter 3. Chapter 4 Conjugate Direction Methods 4.1 Conjugate Gradient Methods. ix xiii 1 3 3 6 11 12 12 16 19


method (DOO) is proved to be globally convergent. Numerical results showed that the algorithm takes lesser number of itera-tions to obtain the minimum of a given function. Keywords and phrases: Unconstrained minimization problem, spectral conjugate gradient method, global convergence 2010 Mathematical Subject Classi cation: 90C25, 90C30 1

Acceleration of the EM Algorithm by Using Quasi-Newton Methods

Jamshidian and Jennrich (1993) proposed a conjugate gradient accelerator for the EM algorithm. This accelerator uses their observation that, close to 0, the EM step g(8) can be viewed as a generalized gradient of the log-likelihood 1(8). It proceeds by applying generalized conjugate gradient methods. In addition to using g(O) this


The conjugate gradient search directions in our method are generated by the following formula dk+1 = ¡ kgk+1 +flksk; k 0 (4) where gk = rE(wk), sk = wk+1 ¡wk, k is a positive multiplier, and d0 = ¡g0. Conjugate gradient methods difier in their choice for the multiplier flk used to construct the search direction.

هموزر - semnan.ac.ir

6. Nasrin Mirhosseini: On a Nonlinear Conjugate Gradient Method which is Globally Convergent for Nonconvex Functions, July 2016. 7. Hossein Mehdizadeh: A Class of Descent Nonlinear Three{Term Conjugate Gradient Methods Based on Secant Conditions, June 2016. 8. Shayesteh Moradi: Some Descent Modi ed Fletcher{Reeves Conjugate Gradient Methods,

Parallel overlapping domain decomposition methods for coupled

systems is a major challenge for any iterative methods. The focus of this paper is to investigate a parallel domain decomposition precondi-tioning technique for the coupled systems. We show that with the powerful domain decomposition based preconditioner the convergence of the iterative methods can

Global Convergence Properties of Conjugate Gradient Methods

jugate gradient methods. Wecall (2.18) the sucient descent condition. The first class ofmethodsweconsider, in 3, is related to the FRmethod. Weshowthat any methodofthe form (1.2)-(] 3) is globally convergent if ksatisfies k. The result readily suggests a new implementation of the PRmethod that preserves its efficiency andassures its convergence.

Preconditioned Conjugate Gradient Algorithms with Column Scaling

conjugate gradient algorithms. I. Introduction We consider the problem min x 2R n f (x ) (1) In general, we assume that the function f is continuously di erentiable, i.e., f 2 C 1. We can use the conjugate gradient algorithm to solve problem (1). In [9] a new family of conjugate gradient algorithms was introduced based on methods proposed in [16].

Masoud Fatemi english cv

7. M. Fatemi, An optimal parameter for dai‐Liao family of conjugate gradient methods, Optim Theory and Appl, (2016) 169(2): 587‐605. 8. M. Fatemi, A new efficient conjugate gradient method for unconstrained optimization, Journal of Comput and Applied Math, (2016) 300: 207‐216. 9. M.

BFGS Method: A New Search Direction

To incorporate more curvature information to the conjugate gradient direction, Birgin and Martinez (2001) proposed to scale the search direction (more precisely, on the steepest descent part g k) by some Rayleigh quotient of the local Hessian, which gives arise a new class of methods called spectral conjugate gradient methods. Surprisingly,

Spectral Projected Gradient Methods - IME-USP

The Spectral Projected Gradient method SPG aims to solve the problem n is closed and convex. ∇f(x)Td ≥0 for all d ∈IRn In [18], SPG method has been presented as a member of a wider family of Inexact Variable Metric methods for solving (7). Let IB be the set of n×n positive definite matrices such that kBk≤L and kB−1k≤L

Another Nonlinear Conjugate Gradient Algorithm for

Liao, New conjugacy conditions and related nonlinear conjugate gradient methods. Appl. Math. Optim., 43 (2001), pp. 87-101.] conjugate gradient algorithm. Close to our computational scheme is the conjugate gradient algorithm recently proposed by Hager and Zhang [W.W. Hager and H. Zhang, A new conjugate gradient method with guaranteed

Preconditioning Nonlinear Conjugate Gradient with

of the linear residual with the gradient of the nonlinear function, such that βFR k = ∥дk ∥2 ∥дk−1∥ 2. (6) Although globally convergent, it has quickly been superseded by faster and more robust NCG methods. We have chosen to include Fletcher-Reeves in our numerical studies because of its historical significance.

A fast spectral conjugate gradient method for solving

This paper proposes a new spectral conjugate gradient (SCG) approach for solving unregulated nonlinear optimization problems. Our approach proposes Using Wolfe's rapid line scan to adjust the standard conjugate descent (CD) algorithm. A new spectral parameter is a mixture of new gradient and old search path.

A Dai Yuan conjugate gradient algorithm with sufficient

The method of (5) (8) is a method that belongs to the family of scaled conjugate gradient methods introduced by Birgin and Mart´ınez [ 3]. Observe that if f is a quadratic function and α k is selected to achieve the exact minimum of


In this paper, we will propose a three-parameter family of conjugate gradient methods, which includes the ve nonlinear conjugate gradient methods mentioned above and the one in [22]. The three-parameter family of methods also has several other families of conjugate gradient methods and some hybrid methods as its special cases (see the next

Gradient Method with Retards and Generalizations

simultaneously in parallel with Xk+1. Observe that, even in the efficient conjugate gradient method, the computation of the steplength associated to the search direction necessarily precedes the computation of the new iterate. In this paper, we prove that the iteration (1.3) is globally convergent to the solution of the problem. From

Algorithm 851: CG DESCENT, a Conjugate Gradient Method with

Algorithm 851: CG DESCENT, a Conjugate Gradient Method with Guaranteed Descent WILLIAM W. HAGER and HONGCHAO ZHANG University of Florida Recently, a new nonlinear conjugate gradient scheme was developed which satisfies the descent condition gT kdk ≤− 7 8 gk 2 and which is globally convergent whenever the line search fulfills the Wolfe

A Modified Conjugate Gradient Method and Its Global Convergence

proved that the family of methods using line searches that satisfy (4) and (7) converges globally if the parameters 1, 2and are such that 1 12 = Based on the above research, Sellami, Laskri and Benzine [4] proposed a new two-parameter family of conjugate gradient methods in which 2 2 111 (1 ) ( ), (1 ) ( )( ) kk k kk k kk k k k kk ggd ggd


A Globally Convergent Conjugate Gradient Method for Minimizing Self-Concordant Functions on Riemannian Manifolds. Submitted to the 2007 IFAC World Congress, July 6- 11, 2008, Seoul, Korea.

The Algorithms of Broyden-CG for Unconstrained Optimization

new algorithm is globally convergent and gratify the sufficient descent condition. Keywords: Broyden method, conjugate gradient method, search direction, global convergent 1 Introduction Consider the unconstrained optimization problems: min xRn fx (1) and let f R R: n o be continuously differentiable. The Broyden s family