Quadratic cost flow and the conjugate gradient method

Sun, Jie; Yang, Xiaoqi; Chen, Xiongda

doi:10.1016/j.ejor.2003.04.003

Cited by 11 publications

(12 citation statements)

References 11 publications

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“…The conjugate gradient method is an approach for solving large scale minimization problems due to its decreased storage requirements and simple computation (e.g. [4,7,12,13,30,31]). This method was motivated by Hestenes and Stiefel in solving symmetric positive definite linear equations [23] and developed by Fletcher and Reeves (e.g.…”

Section: Introductionmentioning

confidence: 99%

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A new family of conjugate gradient methods

Shi

Guo

2009

Journal of Computational and Applied Mathematics

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a b s t r a c tIn this paper we develop a new class of conjugate gradient methods for unconstrained optimization problems. A new nonmonotone line search technique is proposed to guarantee the global convergence of these conjugate gradient methods under some mild conditions. In particular, Polak-Ribiére-Polyak and Liu-Storey conjugate gradient methods are special cases of the new class of conjugate gradient methods. By estimating the local Lipschitz constant of the derivative of objective functions, we can find an adequate step size and substantially decrease the function evaluations at each iteration. Numerical results show that these new conjugate gradient methods are effective in minimizing large-scale non-convex non-quadratic functions.

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Section: Introductionmentioning

confidence: 99%

“…We can find some splendid literature on conjugate gradient method, e.g. [4,5,7,10,11,14,15,24,25,30,31,44]. However, to the best of our knowledge, the global convergence of PRP, LS and HS methods has not been established under all mentioned line searches.…”

Section: Introductionmentioning

confidence: 99%

A new family of conjugate gradient methods

Shi

Guo

2009

Journal of Computational and Applied Mathematics

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“…Although out of the scope of this paper, based on the conjugate gradient methodology there are linesearch procedures for unconstrained optimization which are useful for solving large scale problems. These methods have well-known convergence properties (see Hager and Zhang (12) and the references therein), and have been used in some practical engineering applications (see, for instance, Sun et al (20)). There are some other works using directions of negative curvature within conjugate gradient schemes (see Sanmatías and Vercher (18) and the references therein).…”

Section: Introductionmentioning

confidence: 99%

Combining and scaling descent and negative curvature directions

et al. 2009

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The aim of this paper is the study of different approaches to combine and scale, in an efficient manner, descent information for the solution of unconstrained optimization problems. We consider the situation in which different directions are available in a given iteration, and we wish to analyze how to combine these directions in order to provide a method more efficient and robust than the standard Newton approach. In particular, we will focus on the scaling process that should be carried out before combining the directions. We derive some theoretical results regarding the conditions necessary to ensure the convergence of combination procedures following schemes similar to our proposals. Finally, we conduct some computational

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“…These methods have well-known convergence properties (see [16], and references therein), and have been used in some practical engineering applications (see, for instance [25]). Other works also use directions of negative curvature within conjugate gradient schemes (see [23] and references therein).…”

Section: Introductionmentioning

confidence: 99%

Nonconvex optimization using negative curvature within a modified linesearch

Olivares

Moguerza

Prieto

2008

European Journal of Operational Research

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This paper describes a new algorithm for the solution of nonconvex unconstrained optimization problems, with the property of converging to points satisfying second order necessary optimality conditions. The algorithm is based on a pro cedure which, from two descent directions, a Newton type direction and a direction of negative curvature, selects in each iteration the linesearch model best adapted to the properties of these directions. The paper also presents results of numeri cal experiments that illustrate its practical efficiency.

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Quadratic cost flow and the conjugate gradient method

Cited by 11 publications

References 11 publications

A new family of conjugate gradient methods

A new family of conjugate gradient methods

Combining and scaling descent and negative curvature directions

Nonconvex optimization using negative curvature within a modified linesearch

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