Nguyen H. Thao

Regularity of collections of sets and convergence of inexact alternating projections

  • Alexander Y. Kruger
  • Nguyen H. Thao
    • Categories Nonsmooth Optimization Tags , , ,

    We study the usage of regularity properties of collections of sets in convergence analysis of alternating projection methods for solving feasibility problems. Several equivalent characterizations of these properties are provided. Two settings of inexact alternating projections are considered and the corresponding convergence estimates are established and discussed. Article Download View Regularity of collections of sets … Read more

    An induction theorem and nonlinear regularity models

  • Phan Q. Khanh
  • Alexander Y. Kruger
  • Nguyen H. Thao
    • Categories Convex and Nonsmooth Optimization Tags , ,

    A general nonlinear regularity model for a set-valued mapping $F:X\times\R_+\rightrightarrows Y$, where $X$ and $Y$ are metric spaces, is considered using special iteration procedures, going back to Banach, Schauder, Lusternik and Graves. Namely, we revise the \emph{induction theorem} from Khanh, \emph{J. Math. Anal. Appl.}, 118 (1986) and employ it to obtain basic estimates for studying … Read more

    About [q]-regularity properties of collections of sets

  • Alexander Y. Kruger
  • Nguyen H. Thao
    • Categories Nonsmooth Optimization

    We examine three primal space local Hoelder type regularity properties of finite collections of sets, namely, [q]-semiregularity, [q]-subregularity, and uniform [q]-regularity as well as their quantitative characterizations. Equivalent metric characterizations of the three mentioned regularity properties as well as a sufficient condition of [q]-subregularity in terms of Frechet normals are established. The relationships between [q]-regularity … Read more

    Quantitative Characterizations of Regularity Properties of Collections of Sets

  • Alexander Y. Kruger
  • Nguyen H. Thao
    • Categories Nonsmooth Optimization

    Several primal and dual characterizations of regularity properties of collections of sets in normed linear spaces are discussed. Relationships between regularity properties of collections of sets and those of set-valued mappings are provided. Citation JOURNAL OF OPTIMIZATION THEORY AND APPLICATIONS (2015) 164:41–67 Article Download View Quantitative Characterizations of Regularity Properties of Collections of Sets

    About uniform regularity of collections of sets

  • Alexander Y. Kruger
  • Nguyen H. Thao
    • Categories Convex and Nonsmooth Optimization Tags ,

    We further investigate the uniform regularity property of collections of sets via primal and dual characterizing constants. These constants play an important role in determining convergence rates of projection algorithms for solving feasibility problems. Citation Published in Serdica Math. J. 39, 287–312 (2013) http://www.math.bas.bg/serdica/2013/2013-287-312.pdf Article Download View About uniform regularity of collections of sets

    Well-posedness for Lexicographic Vector Equilibrium Problems

  • L. Q. Anh
  • Alexander Y. Kruger
  • T. Q. Duy
  • Nguyen H. Thao
    • Categories Multi-Criteria Optimization, Nonsmooth Optimization Tags , ,

    We consider lexicographic vector equilibrium problems in metric spaces. Sufficient conditions for a family of such problems to be (uniquely) well-posed at the reference point are established. As an application, we derive several results on well-posedness for a class of variational inequalities. Citation Published in Constructive Nonsmooth Analysis and Related Topics (Vladimir Demyanov, Panos M. … Read more