Nonlinear error bounds for quasiconvex inequality systems

Optimization letters 11 巻 1 号 107-120 頁 2017-01 発行
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タイトル
Nonlinear error bounds for quasiconvex inequality systems
著者
収録物名
Optimization letters
11
1
開始ページ 107
終了ページ 120
収録物識別子
ISSN 18624472
内容記述
その他
The error bound is an inequality that restricts the distance from a vector to a given set by a residual function. The error bound has so many useful applications, for example in variational analysis, in convergence analysis of algorithms, in sensitivity analysis, and so on. For convex inequality systems, Lipschitzian error bounds are studied mainly. If an inequality system is not convex, it is difficult to show the existence of a Lipschitzian global error bound in general. Hence for nonconvex inequality systems, Holderian error bounds and nonlinear error bounds have been investigated. For quasiconvex inequality systems, there are so many examples such that systems do not have Lipschitzian and Holderian error bounds. However, the research of nonlinear error bounds for quasiconvex inequality systems have not been investigated yet as far as we know. In this paper, we study nonlinear error bounds for quasiconvex inequality systems. We show the existence of a global nonlinear error bound by a generator of a quasiconvex function and a constraint qualification. We show well-posedness of a quasiconvex function by the error bound.
主題
Nonlinear error bound ( その他)
Quasiconvex inequality system ( その他)
Generator of a quasiconvex ( その他)
function ( その他)
Constraint qualification ( その他)
Well-posedness ( その他)
言語
英語
資源タイプ 学術雑誌論文
出版者
Springer
発行日 2017-01
権利情報
The final publication is available at Springer via http://dx.doi.org/10.1007/s11590-015-0992-2. © Springer-Verlag Berlin Heidelberg 2015.
出版タイプ Accepted Manuscript(出版雑誌の一論文として受付されたもの。内容とレイアウトは出版社の投稿様式に沿ったもの)
アクセス権 オープンアクセス
関連情報
[DOI] 10.1007/s11590-015-0992-2
[NCID] AA12249544