55 citations · 200 across the 10 of their papers we have counts for
11 papers
Sequential Extremal Principle: Refinements and Applications
Nguyen Duy Cuong, Alexander Kruger, Nguyen Hieu Thao
Sequential extremality and stationarity properties are discussed with the emphasis on those corresponding to fixed sequences of translations. Exact quantitative characterisations o…
Extremality of families of sets and set-valued optimization
Nguyen Duy Cuong, Alexander Y. Kruger, Nguyen Hieu Thao
The paper explores a new extremality model involving collections of arbitrary families of sets. We demonstrate its applicability to set-valued optimization problems with general pr…
Extremality of families of sets
Nguyen Duy Cuong, Alexander Y. Kruger, Nguyen Hieu Thao
The paper proposes another extension of the extremal principle. A new extremality model involving collections of arbitrary families of sets is studied. It generalizes the conventio…
Projection methods for high numerical aperture phase retrieval
Nguyen Hieu Thao, Oleg Soloviev, Russell Luke +1
We develop for the first time a mathematical framework in which the class of projection algorithms can be applied to high numerical aperture (NA) phase retrieval. Within this frame…
A convergent relaxation of the Douglas-Rachford algorithm
Nguyen Hieu Thao
This paper proposes an algorithm for solving structured optimization problems, which covers both the backward-backward and the Douglas-Rachford algorithms as special cases, and ana…
Necessary conditions for linear convergence of iterated expansive, set-valued mappings with application to alternating projections
D. Russell Luke, Marc Teboulle, Nguyen H. Thao
We present necessary conditions for monotonicity, in one form or another, of fixed point iterations of mappings that violate the usual nonexpansive property. We show that most reas…
Quantitative convergence analysis of iterated expansive, set-valued mappings
D. Russell Luke, Nguyen H. Thao, Matthew K. Tam
We develop a framework for quantitative convergence analysis of Picard iterations of expansive set-valued fixed point mappings. There are two key components of the analysis. The fi…
Set Regularities and Feasibility Problems
Alexander Y. Kruger, D. Russell Luke, Nguyen H. Thao
We synthesize and unify notions of regularity, both of individual sets and of collections of sets, as they appear in the convergence theory of projection methods for consistent fea…
An induction theorem and nonlinear regularity models
Phan Q. Khanh, Alexander Y. Kruger, Nguyen H. Thao
A general nonlinear regularity model for a set-valued mapping , where and are metric spaces, is considered using special iteration procedu…
Quantitative Characterizations of Regularity Properties of Collections of Sets
Alexander Kruger, Nguyen Hieu Thao
Several primal and dual characterizations of regularity properties of collections of sets in normed linear spaces are discussed. Relationships between regularity properties of coll…
About uniform regularity of collections of sets
Alexander Y. Kruger, Nguyen H. Thao
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 co…