A New Supermemory Gradient Method without Line Search for Unconstrained Optimization

Liu, June; Liu, Huanbin; Zheng, Yue

doi:10.1007/978-3-642-01216-7_68

Cited by 3 publications

(2 citation statements)

References 11 publications

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“…In the particular case of modern SMG algorithms [41][42][43][44], s k is computed in two steps. First, a descent direction is constructed by combining the vectors d i k with some predefined weights.…”

Section: B Stepsize Strategiesmentioning

confidence: 99%

A Majorize–Minimize Strategy for Subspace Optimization Applied to Image Restoration

Chouzenoux

Idier

Moussaoui

2011

IEEE Trans. on Image Process.

130

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This paper proposes accelerated subspace optimization methods in the context of image restoration. Subspace optimization methods belong to the class of iterative descent algorithms for unconstrained optimization. At each iteration of such methods, a stepsize vector allowing the best combination of several search directions is computed through a multidimensional search. It is usually obtained by an inner iterative second-order method ruled by a stopping criterion that guarantees the convergence of the outer algorithm. As an alternative, we propose an original multidimensional search strategy based on the majorize-minimize principle. It leads to a closed-form stepsize formula that ensures the convergence of the subspace algorithm whatever the number of inner iterations. The practical efficiency of the proposed scheme is illustrated in the context of edge-preserving image restoration.

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Section: B Stepsize Strategiesmentioning

confidence: 99%

A Majorize–Minimize Strategy for Subspace Optimization Applied to Image Restoration

Chouzenoux

Idier

Moussaoui

2011

IEEE Trans. on Image Process.

130

View full text Add to dashboard Cite

show abstract

“…If B k = 1/ᾱ BB k I is chosen, whereᾱ BB k is some modified BB stepsize, then the α AOS k reduces toᾱ BB k , and the corresponding method is some modified BB method [4,7,30]. And if B k = 1/tI, t > 0, then the α AOS k is the fixed stepsize t, and the corresponding method is the gradient method with fixed stepsize [16,22,33]. In this sense, the approximate optimal gradient method is a generalisation of the BB methods.…”

Section: Introductionmentioning

confidence: 99%

The new spectral conjugate gradient method for large-scale unconstrained optimisation

et al. 2020

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The spectral conjugate gradient methods are very interesting and have been proved to be effective for strictly convex quadratic minimisation. In this paper, a new spectral conjugate gradient method is proposed to solve large-scale unconstrained optimisation problems. Motivated by the advantages of approximate optimal stepsize strategy used in the gradient method, we design a new scheme for the choices of the spectral and conjugate parameters. Furthermore, the new search direction satisfies the spectral property and sufficient descent condition. Under some suitable assumptions, the global convergence of the developed method is established. Numerical comparisons show better behaviour of the proposed method with respect to some existing methods for a set of 130 test problems.

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A new supermemory gradient method for unconstrained optimization problems

Guan-shu

2011

Optim Lett

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A New Supermemory Gradient Method without Line Search for Unconstrained Optimization

Cited by 3 publications

References 11 publications

A Majorize–Minimize Strategy for Subspace Optimization Applied to Image Restoration

A Majorize–Minimize Strategy for Subspace Optimization Applied to Image Restoration

The new spectral conjugate gradient method for large-scale unconstrained optimisation

A new supermemory gradient method for unconstrained optimization problems

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