26,413 research outputs found
Convergence and stability of line search methods for unconstrained optimization.
This paper explores the stability of general line search methods in the sense of Lyapunov, for minimizing a smooth nonlinear function. In particular we give sufficient conditions for a line search method to be globally asymptotical stable. Our analysis suggests that the proposed sufficient conditions for asymptotical stability is equivalent to the Zoutendijk-type conditions in conventional global convergence analysis
A three-term conjugate gradient method with nonmonotone line search for unconstrained optimization
The technique of nonmontone line search has received much attention in nonlinear optimization. This technique can improve the computational cost of the line search process and increase the rate of convergence of the algorithm. However, the convergence of this line search scheme utilizes some rather restrictive assumption concerning the search directions, which may not hold for most conjugate gradient methods. Thus in this paper, we propose a three-term conjugate gradient method with nonmonotone backtracking line search technique for solving large scale unconstrained optimization problems. Convergence analysis of the proposed method is established under reasonable conditions. Numerical experiments carried out on benchmark test problems has clearly indicated the effectiveness of the developed algorithm in terms of efficiency and robustness
Nonlinear Conjugate Gradient Methods with Wolfe Type Line Search
Nonlinear conjugate gradient method is one of the useful methods for unconstrained
optimization problems. In this paper, we consider three kinds of nonlinear
conjugate gradient methods with Wolfe type line search for unstrained optimization problems.
Under some mild assumptions, the global convergence results of the given methods
are proposed. The numerical results show that the nonlinear conjugate gradient methods
with Wolfe type line search are efficient for some unconstrained optimization problems
Global Convergence of a Nonlinear Conjugate Gradient Method
A modified PRP nonlinear conjugate gradient method to solve unconstrained optimization problems is proposed. The important property of the proposed method is that the sufficient descent property is guaranteed independent of any line search. By the use of the Wolfe line search, the global convergence of the proposed method is established for nonconvex minimization. Numerical results show that the proposed method is effective and promising by comparing with the VPRP, CG-DESCENT, and DL+ methods
New Inexact Line Search Method for Unconstrained Optimization
We propose a new inexact line search rule and analyze the global convergence and convergence rate of related descent methods. The new line search rule is similar to the Armijo line-search rule and contains it as a special case. We can choose a larger stepsize in each line-search procedure and maintain the global convergence of related line-search methods. This idea can make us design new line-search methods in some wider sense. In some special cases, the new descent method can reduce to the Barzilai and Borewein method. Numerical results show that the new line-search methods are efficient for solving unconstrained optimization problems.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/45195/1/10957_2005_Article_6553.pd
Forward-backward truncated Newton methods for convex composite optimization
This paper proposes two proximal Newton-CG methods for convex nonsmooth
optimization problems in composite form. The algorithms are based on a a
reformulation of the original nonsmooth problem as the unconstrained
minimization of a continuously differentiable function, namely the
forward-backward envelope (FBE). The first algorithm is based on a standard
line search strategy, whereas the second one combines the global efficiency
estimates of the corresponding first-order methods, while achieving fast
asymptotic convergence rates. Furthermore, they are computationally attractive
since each Newton iteration requires the approximate solution of a linear
system of usually small dimension
A COMPARATIVE STUDY OF SOME MODIFICATIONS OF CG METHODS UNDER EXACT LINE SEARCH
Conjugate Gradient (CG) method is a technique used in solving nonlinear unconstrained optimization problems. In this paper, we analysed the performance of two modifications and compared the results with the classical conjugate gradient methods of. These proposed methods possesse global convergence properties for general functions using exact line search. Numerical experiments show that the two modifications are more efficient for the test problems compared to classical CG coefficients
Stability Analysis Of Continuous Conjugate Gradient Method
Kaedah Conjugate Gradient adalah sangat berguna untuk: menyelesaikan masalah
tiada kekangan paling optimum yang berskala besar. Walaubagaimanapun, carlan
garis (line search) dalam Kaedah Conjugate Gradient kadang-kadang sukar didapati
dan pengiraannya menggunakan komputer adalah sangat mahal. Berdasarkan
penyelidikan oleh Sun dan Zhang [J. Sun and J. Zhang (2001), Global convergence
of conjugate gradient methods without line search], menyatakan bahawa Kaedah
Conjugate Gradient adalah menumpu secara global (globally convergence) dengan
menggunakan langkah (stepsize) ak yang ditetapkan berdasarkan formula
8r/ ft. Darlpada keputusan yang didapati, mereka mencadangkan carlan
Ilpkll{4
garis (line search) adalah tidak diperlukan untuk mendapatkan penumpuan secara
global (globally convergence) oleh Kaedah Conjugate Gradient. Oleh itu, objektif
disertasi ini adalah untuk menentukan julat a dan P di mana julat ini akan
memastikan kestabilan Kaedah Conjugate Gradient.
In order to solve a large-scale unconstrained optimization, Conjugate Gradient
Method has been proven to be successful. However, the line search required in
Conjugate Gradient Method is sometimes extremely difficult and computationally
expensive. Studies conducted by Sun and Zhang [J. Sun and J. Zhang (2001), Global
convergence of conjugate gradient methods without line search], claimed that the
Conjugate Gradient Method was globally convergence using "fixed" stepsize at
determined using formula at = 8rk
T fk . The result suggested that for global
Ilpkl~
convergence of Conjugate Gradient Method, line search was not compUlsory.
Therefore, tlfts dissertation's objective is to determine the range of a and P where
this range will ensure the stability of Conjugate Gradient Method
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