The Lipschitz continuity of the metric projection

Abatzoglou, Theagenis J.

doi:10.1016/0021-9045(79)90059-5

Cited by 9 publications

(3 citation statements)

References 6 publications

Supporting

Mentioning

Contrasting

Unclassified

Order By: Relevance

“…Замечание 1. В работе [8] аналогичная оценка была получена для выпуклых множеств с C 2 гладкой границей.…”

Section: вспомогательные результатыunclassified

Gradient Projection Algorithm for Strongly Convex Set

Golubev¹

2013

MMI

View full text Add to dashboard Cite

В работе рассматривается стандартный метод проекции градиента в случае, когда множество является R-сильно выпуклым, а функция выпукла, дифференцируема и имеет липшицев градиент. Доказано, что при некоторых естественных дополнительных условиях метод сходится со скоростью геометрической прогрессии.Ключевые слова: гильбертово пространство, метод проекции градиента, метрическая проекция, R-сильно выпуклое множество.

show abstract

“…Замечание 1. В работе [8] аналогичная оценка была получена для выпуклых множеств с C 2 гладкой границей.…”

Section: вспомогательные результатыunclassified

Gradient Projection Algorithm for Strongly Convex Set

Golubev¹

2013

MMI

View full text Add to dashboard Cite

show abstract

“…re [0,1] This allows us to prove: Proof Using Proposition 3.1 we can parameterize P by its reduced arc length ~7. Let v', v" be two consecutive values of g for which P(g) = X; the Taylor formula yields…”

Section: A( V) II Vmentioning

confidence: 99%

“…The two domains have evolved quite independently: approximation theory has developed mathematical tools for the study of the fundamental properties of (1.1), such as existence and uniqueness of 2, continuity and differentiability of the z ~ q~(2) solution, based mainly on a geometrical study of the variety q~(N") in term of its radii of curvature (see, for example, [1] and [2]). …”

Section: Introductionmentioning

confidence: 99%

Quasi-convex sets and size � curvature condition, application to nonlinear inversion

Chavent

1991

Appl Math Optim

View full text Add to dashboard Cite

Abstract. We define a family of sets of a Hilbert space ("quasi-convex sets") on which a generalization of the usual theory of projection on convex sets can be defined (existence, uniqueness, and stability of the projection of all points of some neighborhood of the set). We then give a constructive sufficient condition, called the size × curvature condition, for a set D to be quasi-convex, which involves radii of curvatures of curves lying on the set D. Finally, we use the above result for the study of nonlinear least-squares problems, as they appear in parameter estimation, for which we give a sufficient condition ensuring existence, uniqueness, and stability.

show abstract

Local Strong Convexity in Hilbert Space

Golubev

2020

Communications in Computer and Information Science

View full text Add to dashboard Cite

The Lipschitz continuity of the metric projection

Cited by 9 publications

References 6 publications

Gradient Projection Algorithm for Strongly Convex Set

Gradient Projection Algorithm for Strongly Convex Set

Quasi-convex sets and size � curvature condition, application to nonlinear inversion

Local Strong Convexity in Hilbert Space

Contact Info

Product

Resources

About