A Nonmonotone Line Search Technique for Newton’s Method

Grippo, Luigi; Lampariello, F.; Lucidi, Stefano

doi:10.1137/0723046

Cited by 1,024 publications

(705 citation statements)

References 6 publications

Supporting

Mentioning

662

Contrasting

Unclassified

Order By: Relevance

“…2 indicate that ACBB is much more efficient than SPG2, while it performed better than PRP+, but not as well as CG DESCENT. From the experience in Raydan (1997), the GBB algorithm, with a traditional non-monotone line search (Grippo et al, 1986), may be affected significantly by nearly singular Hessians at the solution. We observe that nearly singular Hessians do not affect ACBB significantly.…”

Section: Numerical Resultsmentioning

confidence: 99%

See 1 more Smart Citation

The cyclic Barzilai-–Borwein method for unconstrained optimization

Dai¹,

Hager²,

Schittkowski³

et al. 2006

IMA Journal of Numerical Analysis

174

163

View full text Add to dashboard Cite

In the cyclic Barzilai-Borwein (CBB) method, the same Barzilai-Borwein (BB) stepsize is reused for m consecutive iterations. It is proved that CBB is locally linearly convergent at a local minimizer with positive definite Hessian. Numerical evidence indicates that when m > n/2 3, where n is the problem dimension, CBB is locally superlinearly convergent. In the special case m = 3 and n = 2, it is proved that the convergence rate is no better than linear, in general. An implementation of the CBB method, called adaptive cyclic Barzilai-Borwein (ACBB), combines a non-monotone line search and an adaptive choice for the cycle length m. In numerical experiments using the CUTEr test problem library, ACBB performs better than the existing BB gradient algorithm, while it is competitive with the well-known PRP+ conjugate gradient algorithm.

show abstract

Section: Numerical Resultsmentioning

confidence: 99%

“…If f r = f (x k ), then the line search is monotone since f (x k+1 ) < f (x k ). The non-monotone line search proposed in Grippo et al (1986) chooses f r to be the maximum function value for the M most recent iterates. That is, at the kth iteration, we have…”

Section: Non-monotone Line Search and Cycle Numbermentioning

confidence: 99%

The cyclic Barzilai-–Borwein method for unconstrained optimization

Dai¹,

Hager²,

Schittkowski³

et al. 2006

IMA Journal of Numerical Analysis

174

163

View full text Add to dashboard Cite

show abstract

“…For a review containing the more recent advances on this special choice of steplength see [20]. The second improvement over traditional gradient projection methods is that a nonmonotone search must be used [10,22]. This feature seems to be essential to preserve the nice and nonmonotone behaviour of the iterates produced by single spectral gradient steps.…”

Section: Introductionmentioning

confidence: 99%

“…. , p and any y 0 ∈ IR n , the sequence {y ℓ i } generated by (22) converges to y * = P Ω (y 0 ) (i.e., y ℓ i − y * → 0 as ℓ → ∞).…”

mentioning

confidence: 99%

Inexact spectral projected gradient methods on convex sets

Birgin¹

2003

IMA Journal of Numerical Analysis

166

178

View full text Add to dashboard Cite

A new method is introduced for large scale convex constrained optimization. The general model algorithm involves, at each iteration, the approximate minimization of a convex quadratic on the feasible set of the original problem and global convergence is obtained by means of nonmonotone line searches. A specific algorithm, the Inexact Spectral Projected Gradient method (ISPG), is implemented using inexact projections computed by Dykstra's alternating projection method and generates interior iterates. The ISPG method is a generalization of the Spectral Projected Gradient method (SPG), but can be used when projections are difficult to compute. Numerical results for constrained least-squares rectangular matrix problems are presented.

show abstract

“…[4,5,6]). The nonmonotone procedure is mainly to choose a large step size for line search methods and avoid the iterates trapped in a narrow curved valley of objective functions.…”

Section: Introductionmentioning

confidence: 99%

Convergence of descent method with new line search

Shi

Shen

2006

J. Appl. Math. Comput.

View full text Add to dashboard Cite

Abstract. An efficient descent method for unconstrained optimization problems is line search method in which the step size is required to choose at each iteration after a descent direction is determined. There are many ways to choose the step sizes, such as the exact line search, Armijo line search, Goldstein line search, and Wolfe line search, etc. In this paper we propose a new inexact line search for a general descent method and establish some global convergence properties. This new line search has many advantages comparing with other similar inexact line searches. Moreover, we analyze the global convergence and local convergence rate of some special descent methods with the new line search. Preliminary numerical results show that the new line search is available and efficient in practical computation.

show abstract

A Nonmonotone Line Search Technique for Newton’s Method

Cited by 1,024 publications

References 6 publications

The cyclic Barzilai-–Borwein method for unconstrained optimization

The cyclic Barzilai-–Borwein method for unconstrained optimization

Inexact spectral projected gradient methods on convex sets

Convergence of descent method with new line search

Contact Info

Product

Resources

About