Fej�r mappings and convex programming

Еремин, И. И.

doi:10.1007/bf00971652

Cited by 23 publications

(13 citation statements)

References 2 publications

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“…arising in hilbertian nonlinear analysis, see for instance [2,5,12,13,14,18,19,30,31,35] and the references therein. In recent years, there have been attempts to generalize standard algorithms such as those discussed in the above references by allowing the underlying metric to vary over the course of the iterations, e.g., [7,10,11,16,26,29].…”

Section: Introductionmentioning

confidence: 99%

Variable metric quasi-Fejér monotonicity

Combettes

Vũ

2013

Nonlinear Analysis: Theory, Methods & Applications

101

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MSC: 65J05 90C25 47H09 Keywords: Convex feasibility problem Convex optimization Hilbert space Inverse problems Proximal Landweber method Proximal point algorithm Quasi-Fejér sequence Variable metricThe notion of quasi-Fejér monotonicity has proven to be an efficient tool to simplify and unify the convergence analysis of various algorithms arising in applied nonlinear analysis. In this paper, we extend this notion in the context of variable metric algorithms, whereby the underlying norm is allowed to vary at each iteration. Applications to convex optimization and inverse problems are demonstrated.

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Section: Introductionmentioning

confidence: 99%

Variable metric quasi-Fejér monotonicity

Combettes

Vũ

2013

Nonlinear Analysis: Theory, Methods & Applications

101

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“…These include, among others, optimization theory (see, e.g., Eremin [33], Censor and Lent [20] and Chinneck [22]), approximation theory (see, e.g., Deutsch [31] and references therein), image reconstruction from projections in computerized tomography (see, e.g., Herman [35, 36]) and control theory (see, e.g., Boyd et al [8]. )…”

Section: Introductionmentioning

confidence: 99%

On The Behavior of Subgradient Projections Methods for Convex Feasibility Problems in Euclidean Spaces

Butnariu¹,

Censor²,

Gurfil³

et al. 2008

SIAM J. Optim.

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We study some methods of subgradient projections for solving a convex feasibility problem with general (not necessarily hyperplanes or half-spaces) convex sets in the inconsistent case and propose a strategy that controls the relaxation parameters in a specific self-adapting manner. This strategy leaves enough user-flexibility but gives a mathematical guarantee for the algorithm’s behavior in the inconsistent case. We present numerical results of computational experiments that illustrate the computational advantage of the new method.

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“…REMARKS 2.2. Some authors do not require nonexpansivity in the definition of attracting mappings; see, for example, Bruck's "strictly quasi-nonexpansive mappings" [18], Elsner, Koltracht, and Neumann's "paracontracting mappings" [51 ], Eremin's "F-weakly Fej6r maps" [52], and Istratescu's "T-mappings" [69,Chap. 6].…”

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confidence: 99%

On Projection Algorithms for Solving Convex Feasibility Problems

1996

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Due to their extraordinary utility and broad applicability in many areas of classical mathematics and modem physical sciences (most notably, computerized tomography), algorithms for solving convex feasibility problems continue to receive great attention. To unify, generalize, and review some of these algorithms, a very broad and flexible framework is investigated. Several crucial new concepts which allow a systematic discussion of questions on behaviour in general Hilbert spaces and on the quality of convergence are brought out. Numerous examples are given.

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Fej�r mappings and convex programming

Cited by 23 publications

References 2 publications

Variable metric quasi-Fejér monotonicity

Variable metric quasi-Fejér monotonicity

On The Behavior of Subgradient Projections Methods for Convex Feasibility Problems in Euclidean Spaces

On Projection Algorithms for Solving Convex Feasibility Problems

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