Conferences/Workshops/Seminars
19-21 Feb. 2018
Variational Analysis Down Under, Federation University Australia
12 Apr. 2018
CIAO Showcase and Workshop, Federation University Australia
Abstract: The extremal principle, a variational counterpart of the convex separation principle in nonconvex settings, lies at the very heart of variational analysis, generalized differentiation theory, nonconvex calculus and optimization-related problems. The talk is devoted to presenting some extended versions of the classical extremal principle as well as their applications in optimization problems.
26 Apr. 2018
CIAO Seminar, Federation University Australia
Abstract: The extremal principle, a variational counterpart of the convex separation principle in nonconvex settings, lies at the very heart of variational analysis, generalized differentiation theory, nonconvex calculus and optimization-related problems. The talk is devoted to presenting some extended versions of the classical extremal principle as well as their applications in optimization problems.
21 May 2018
Workshop on Fixed Points and Applications, RMIT University, Australia
9th Vietnam Mathematical Congress, Vietnam
14-18 Aug. 2018
Abstract: In this talk, we discuss nonlinear transversality properties of collections of sets in normed linear spaces. Equivalent metric characterizations of these properties are established. Dual sufficient conditions for the nonlinear subtransversality are discussed. Relationships between nonlinear transversality properties of collections of sets and the corresponding regularity properties of set-valued mappings are examined.
25 Oct. 2018
CIAO Seminar, Federation University Australia
Abstract: Error bounds play an important role in sensitivity analysis and convergence analysis of computational algorithms. In some cases, it is useful to study general nonlinear error bounds when the conventional linear error bounds do not hold. In this talk, we introduce a nonlinear parametric error bound model and provide some basic tools to study this property. As applications, we will show that nonlinear parametric error bounds can be used to establish necessary and/or sufficient conditions for nonlinear (graph) regularity properties of set-valued mappings as well as nonlinear transversality properties of collections of sets.
3rd WoMBaT, Deakin University Australia
Abstract: In this talk, we discuss nonlinear transversality properties of collections of sets in normed linear spaces. Equivalent metric characterizations of these properties are established. Dual sufficient conditions for the nonlinear subtransversality are discussed. Relationships between nonlinear transversality properties of collections of sets and the corresponding regularity properties of set-valued mappings are examined.
4-7 Dec. 2018
62nd Annual Meeting of the Australian Mathematical Society,
The University of Adelaide, Australia
Abstract: Error bounds play an important role in sensitivity analysis and convergence analysis of computational algorithms. In some cases, it is useful to study general nonlinear error bounds when the conventional linear error bounds do not hold. In this talk, we discuss a nonlinear parametric error bound model for lower semicontinuous functions in metric or Banach/Asplund spaces and provide some basic tools to study this property. As applications, we will show that nonlinear parametric error bounds can be used to establish necessary and/or sufficient conditions for nonlinear (graph) regularity properties of set-valued mappings as well as nonlinear transversality properties of collections of sets.
15 Jan. 2019
Confirmation of Candidature, Federation University Australia
Abstract: Transversality, regularity and error bounds are cornerstones in variational analysis and optimization. They have been powerful tools for establishing optimality conditions in constraint optimization, subdifferential, normal cone and coderivative calculus, and for studying sensitivity analysis and convergence analysis of computational algorithms. In this talk, I summarize what I have done in my first year and establish research questions for my future study.
2 May 2019
SEIT Seminar, Federation University Australia
Abstract: Error bounds play an important role in sensitivity analysis and convergence analysis of computational algorithms. In some cases, it is useful to study general nonlinear error bounds when the conventional linear error bounds do not hold. In this talk, we introduce a nonlinear error bound model that covers two important cases: linear and Holder error bounds. Employing advanced tools in variational analysis, we provide two different dual sufficient conditions for the nonlinear error bounds: first-order conditions and second-order ones. The first-order conditions are presented in terms of Clarke and Fréchet subdifferentials in Banach/Asplund spaces, while the second-order conditions are provided by using proximal subdifferentials in Hilbert spaces.
3-6 Dec. 2019
63nd Annual Meeting of the Australian Mathematical Society, Monash University, Australia
Abstract: In this talk, we discuss primal and dual sufficient conditions for Robinson regularity properties of implicit multifunctions in normed (in particular, Banach/Asplund) spaces. These results are presented in terms of slopes and Clarke/Fréchet subdifferentials and normals. These types of conditions are often overlooked depsite appearing implicitly in proofs of many satements in the literature. We make an attempt to present the conditions explicitly. Interestingly, we prove that these conditions become necessary for the properties in the convex setting. As applications, we establish primal and dual characterizations of the conventional metric regularity properties of set-valued mappings as well as stability properties of a solution mapping of a semi-infinite multiobjective optimization problem.
8-10 Dec. 2019
4th WoMBaT, Swinburne University of Technology, Australia
Abstract: In this talk, we discuss primal and dual necessary and sufficient conditions for a new property so-called "semitransversality of collections of set-valued mappings", which has a strong connection the local extremality of collections of set-valued mappings introduced by Mordukhovich et al. (SIAM J. Optim., 14(2):359–379, 2003) and can be seen as a natural extension of semitransversality of collections of sets (Kruger, A.Y., Thao, N.H., J. Optim. Theory Appl., 164(1):41–67, 2015). Examples are provided to illustrate the property. Connections between the property and semiregularity of set-valued mappings are also discussed.
30 Nov. - 4 Dec. 2020
8-10 Dec. 2020
24 Feb. 2021
Invited talk: Necessary conditions for transversality properties of
collections of sets
Abstract: Transversality properties of collections of sets play an important role in optimization and variational analysis, e.g., as constraint qualifications, qualification conditions in subdifferential, normal cone and coderivative calculus, and convergence analysis of computational algorithms. In this talk, we present some new results on primal (geometric, metric, slope) and dual (subdifferential, normal cone) necessary (in some cases also sufficient) conditions for transversality properties in both linear and nonlinear settings. Quantitative relations between transversality properties and the corresponding regularity properties of set-valued mappings are also discussed.