Minh Bui

College of Sciences

Works (9)

Updated: September 30th, 2024 16:19

2024 article

Integral Resolvent and Proximal Mixtures

Bui, M. N., & Combettes, P. L. (2024, August 24). JOURNAL OF OPTIMIZATION THEORY AND APPLICATIONS, Vol. 8.

By: M. Bui* & P. Combettes n 

author keywords: Hilbert direct integral; Integral proximal mixture; Integral resolvent mixture; Monotone operator; Proximal expectation; Resolvent expectation
Sources: Web Of Science, NC State University Libraries
Added: September 3, 2024

2022 journal article

Projective Splitting as a Warped Proximal Algorithm

APPLIED MATHEMATICS AND OPTIMIZATION, 85(2).

By: M. Bui n

author keywords: Warped proximal algorithm; Projective splitting; Primal-dual algorithm; Splitting algorithm; Monotone inclusion; Monotone operator
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10. Reduced Inequalities (Web of Science)
Source: Web Of Science
Added: May 2, 2022

2021 journal article

A decomposition method for solving multicommodity network equilibria

OPERATIONS RESEARCH LETTERS, 50(1), 40–44.

By: M. Bui n

author keywords: Network equilibrium; Network flow; Traffic assignment; Splitting algorithm; Block-iterative algorithm; Monotone operator
TL;DR: A flexible numerical method based on the asynchronous block-iterative decomposition framework of [6] for solving the multicommodity network equilibrium problem proposed by Rockafellar in 1995 is devised. (via Semantic Scholar)
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10. Reduced Inequalities (Web of Science)
Source: Web Of Science
Added: May 23, 2022

2021 article

Multivariate Monotone Inclusions in Saddle Form

Bui, M. N., & Combettes, P. L. (2021, December 21). MATHEMATICS OF OPERATIONS RESEARCH, Vol. 12.

By: M. Bui n & P. Combettes n 

author keywords: monotone inclusion; monotone operator; saddle form; operator splitting; block-iterative algorithm; asynchronous algorithm; strong convergence
TL;DR: A novel approach to monotone operator splitting based on the notion of a saddle operator, which achieves full splitting, exploits the specific attributes of each operator, is asynchronous, and requires to activate only blocks of operators at each iteration, as opposed to activating all of them. (via Semantic Scholar)
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10. Reduced Inequalities (Web of Science; OpenAlex)
Sources: Web Of Science, NC State University Libraries
Added: January 10, 2022

2020 journal article

Bregman Forward-Backward Operator Splitting

Set-Valued and Variational Analysis, 29(3), 583–603.

By: M. Bui n & P. Combettes n 

author keywords: Banach space; Bregman distance; Forward-backward splitting; Legendre function; Monotone operator
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10. Reduced Inequalities (Web of Science)
Sources: Web Of Science, NC State University Libraries, ORCID
Added: December 21, 2020

2020 journal article

The Douglas--Rachford Algorithm Converges Only Weakly

SIAM Journal on Control and Optimization, 58(2), 1118–1120.

By: M. Bùi* & P. Combettes* 

author keywords: Douglas-Rachford algorithm; method of partial inverses; monotone operator; operator splitting; strong convergence
TL;DR: It is shown that the weak convergence of the Douglas--Rachford algorithm for finding a zero of the sum of two maximally monotone operators cannot be improved to strong convergence and strong convergence can fail for the method of partial inverses. (via Semantic Scholar)
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10. Reduced Inequalities (Web of Science)
Sources: Web Of Science, Crossref, NC State University Libraries
Added: July 20, 2020

2020 journal article

Warped proximal iterations for monotone inclusions

Journal of Mathematical Analysis and Applications, 491(1), 124315.

By: M. Bùi n & P. Combettes n 

author keywords: Monotone inclusion; Operator splitting; Strong convergence; Warped resolvent; Warped proximal iterations
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UN Sustainable Development Goal Categories
10. Reduced Inequalities (Web of Science; OpenAlex)
Sources: Web Of Science, Crossref, NC State University Libraries
Added: August 10, 2020

2019 journal article

Applying FISTA to optimization problems (with or) without minimizers

MATHEMATICAL PROGRAMMING, 184(1-2), 349–381.

By: H. Bauschke *, M. Bui n & X. Wang *

author keywords: Convex function; FISTA; Forward-backward method; Nesterov acceleration; Proximal gradient algorithm
TL;DR: This work systematically study FISTA and its variants and presents general results that are applicable, regardless of the existence of minimizers. (via Semantic Scholar)
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10. Reduced Inequalities (Web of Science)
Source: Web Of Science
Added: November 2, 2020

2019 journal article

On sums and convex combinations of projectors onto convex sets

JOURNAL OF APPROXIMATION THEORY, 242, 31–57.

By: H. Bauschke *, M. Bui n & X. Wang *

author keywords: Convex set; Convex cone; Convex combination; Projection operator; Projector; Sum of projectors; Partial sum property; Monotone operator; Proximity operator
TL;DR: This work provides a complete answer to the question of characterizing the instances where the projector onto the Minkowski sum of closed convex sets is generally not equal to the sum of individual projectors. (via Semantic Scholar)
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10. Reduced Inequalities (Web of Science)
Source: Web Of Science
Added: June 17, 2019

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