2 citations · 8 across the 15 of their papers we have counts for
19 papers
Variational Analysis in Spectral Decomposition Systems
Hòa T. Bùi, Minh N. Bùi, Christian Clason
This work is concerned with the variational analysis of functions defined on Euclidean spaces whose values depend solely on certain invariants (``spectrum'') of their arguments, a…
A Block-Activated Decomposition Algorithm for Multi-Stage Stochastic Variational Inequalities
Minh N. Bùi
We develop a block-activated decomposition algorithm for multi-stage stochastic variational inequalities with nonanticipativity constraints. The algorithm features two computationa…
Convex Analysis in Spectral Decomposition Systems
Hòa T. Bùi, Minh N. Bùi, Christian Clason
This work is concerned with the convex analysis of functions defined on (not necessarily finite-dimensional) Hilbert spaces whose values depend solely on a certain ``spectrum'' of…
On a Lemma by Brézis and Haraux
Minh N. Bùi
We propose several applications of an often overlooked part of the 1976 paper by Brézis and Haraux, in which the Brézis--Haraux theorem was established. Our results unify and exten…
Integral Resolvent and Proximal Mixtures
Minh N. Bùi, Patrick L. Combettes
Using the theory of Hilbert direct integrals, we introduce and study a monotonicity-preserving operation, termed the integral resolvent mixture. It combines arbitrary families of m…
Hilbert Direct Integrals of Monotone Operators
Minh N. Bùi, Patrick L. Combettes
Finite Cartesian products of operators play a central role in monotone operator theory and its applications. Extending such products to arbitrary families of operators acting on di…
Interchange Rules for Integral Functions
Minh N. Bùi, Patrick L. Combettes
We first present an abstract principle for the interchange of infimization and integration over spaces of mappings taking values in topological spaces. New conditions on the underl…
Analysis and Numerical Solution of a Modular Convex Nash Equilibrium Problem
Minh N. Bùi, Patrick L. Combettes
We investigate a modular convex Nash equilibrium problem involving nonsmooth functions acting on linear mixtures of strategies, as well as smooth coupling functions. An asynchronou…
A Decomposition Method for Solving Multicommodity Network Equilibrium
Minh N. Bùi
We consider the numerical aspect of the multicommodity network equilibrium problem proposed by Rockafellar in 1995. Our method relies on the flexible monotone operator splitting fr…
Projective Splitting as a Warped Proximal Algorithm
Minh N. Bùi
We show that the asynchronous block-iterative primal-dual projective splitting framework introduced by P. L. Combettes and J. Eckstein in their 2018 Math. Program. paper can be vie…
Block-Activated Algorithms for Multicomponent Fully Nonsmooth Minimization
Minh N. Bùi, Patrick L. Combettes, Zev C. Woodstock
Under consideration are multicomponent minimization problems involving a separable nonsmooth convex function penalizing the components individually, and nonsmooth convex coupling t…
A Warped Resolvent Algorithm to Construct Nash Equilibria
Minh N. Bùi, Patrick L. Combettes
We propose an asynchronous block-iterative decomposition algorithm to solve Nash equilibrium problems involving a mix of nonsmooth and smooth functions acting on linear mixtures of…
Multivariate Monotone Inclusions in Saddle Form
Minh N. Bùi, Patrick L. Combettes
We propose a novel approach to monotone operator splitting based on the notion of a saddle operator. Under investigation is a highly structured multivariate monotone inclusion prob…
The Douglas--Rachford Algorithm Converges Only Weakly
Minh N. Bùi, Patrick L. Combettes
We show 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. Lik…
Warped Proximal Iterations for Monotone Inclusions
Minh N. Bùi, Patrick L. Combettes
Resolvents of set-valued operators play a central role in various branches of mathematics and in particular in the design and the analysis of splitting algorithms for solving monot…
Bregman Forward-Backward Operator Splitting
Minh N. Bùi, Patrick L. Combettes
We establish the convergence of the forward-backward splitting algorithm based on Bregman distances for the sum of two monotone operators in reflexive Banach spaces. Even in Euclid…
Applying FISTA to optimization problems (with or) without minimizers
Heinz H. Bauschke, Minh N. Bui, Xianfu Wang
Beck and Teboulle's FISTA method for finding a minimizer of the sum of two convex functions, one of which has a Lipschitz continuous gradient whereas the other may be nonsmooth, is…
On sums and convex combinations of projectors onto convex sets
Heinz H. Bauschke, Minh N. Bui, Xianfu Wang
The projector onto the Minkowski sum of closed convex sets is generally not equal to the sum of individual projectors. In this work, we provide a complete answer to the question of…
Projecting onto the intersection of a cone and a sphere
Heinz H. Bauschke, Minh N. Bui, Xianfu Wang
The projection onto the intersection of sets generally does not allow for a closed form even when the individual projection operators have explicit descriptions. In this work, we s…