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Papers by Regina Burachik

Research paper thumbnail of Strong duality for generalized monotropic programming in infinite dimensions

Fenchel duality Epigraph of a convex function Conjugate function a b s t r a c t We establish dua... more Fenchel duality Epigraph of a convex function Conjugate function a b s t r a c t We establish duality results for the generalized monotropic programming problem in separated locally convex spaces. We formulate the generalized monotropic programming (GMP) as the minimization of a (possibly infinite) sum of separable proper convex functions, restricted to a closed and convex cone. We obtain strong duality under a constraint qualification based on the closedness of the sum of the epigraphs of the conjugates of the convex functions. When the objective function is the sum of finitely many proper closed convex functions, we consider two types of constraint qualifications, both of which extend those introduced in the literature. The first constraint qualification ensures strong duality, and is equivalent to the one introduced by Boţ and Wanka. The second constraint qualification is an extension of Bertsekas' constraint qualification and we use it to prove zero duality gap.

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Research paper thumbnail of The joint EUROPT-OMS conference on optimization, Prague, Czech Republic, July 4–7, 2007, Part I

Optimization Methods and Software

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Research paper thumbnail of The joint EUROPT-OMS conference on optimization, Prague, Czech Republic, July 4–7, 2007. Part II

Optimization Methods and Software

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Research paper thumbnail of On a Modified Subgradient Algorithm for Dual Problems via Sharp Augmented Lagrangian*

Journal of Global Optimization, 2006

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Research paper thumbnail of Generalized proximal point methods for the variational inequality problem

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Research paper thumbnail of On primal convergence for augmented Lagrangian duality

Http Dx Doi Org 10 1080 02331934 2010 527971, Aug 1, 2011

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Research paper thumbnail of Corrigendum to: “On a family of convex functions associated to subdifferentials”

Journal of nonlinear and convex analysis

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Research paper thumbnail of Set-valued mappings and enlargement of monotone operators

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Research paper thumbnail of Operating enlargements of monotone operators: new connections with convex functions

Pacific Journal of Mathematics

Given a maximal monotone operator T in a Banach space, a family of enlargements E(T) of T has bee... more Given a maximal monotone operator T in a Banach space, a family of enlargements E(T) of T has been introduced by Svaiter. He also defined a sum and a positive scalar multiplication of enlargements. The first aim of this work is to further study the properties of these operations. Burachik and Svaiter studied a family of convex functions H(T) which is in a one to one correspondence with E(T). The second

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Research paper thumbnail of Set-valued mappings & enlargements of monotone operators

This book is addressed to mathematicians, engineers, economists, and researchers interested in ac... more This book is addressed to mathematicians, engineers, economists, and researchers interested in acquiring a solid mathematical foundation in topics such as point-to-set operators, variational inequalities, general equilibrium theory, and nonsmooth optimization, among others. Containing extensive exercises and examples throughout the text, the first four chapters of the book can also be used for a one-quarter course in set-valued analysis and maximal monotone operators for graduate students in pure and applied mathematics, mathematical economics, operations research and related areas. The only requisites, besides a minimum level of mathematical maturity, are some basic results of general topology and functional analysis.

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Research paper thumbnail of An Additive Subfamily of Enlargements of a Maximally Monotone Operator

Set-Valued and Variational Analysis, 2015

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Research paper thumbnail of Enlargements of Monotone Operators

Optimization and Its Applications, 2008

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Research paper thumbnail of Convex Analysis and Fixed Point Theorems

Optimization and Its Applications, 2008

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Research paper thumbnail of Set Convergence and Point-to-Set Mappings

Optimization and Its Applications, 2008

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Research paper thumbnail of Recent Topics in Proximal Theory

Optimization and Its Applications, 2008

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Research paper thumbnail of ε-Enlargements of Maximal Monotone Operators: Theory and Applications

Applied Optimization, 1998

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Research paper thumbnail of Monotone Operators Without Enlargements

Springer Proceedings in Mathematics & Statistics, 2013

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Research paper thumbnail of A Deflected Subgradient Method Using a General Augmented Lagrangian Duality with Implications on Penalty Methods

Springer Optimization and Its Applications, 2010

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Research paper thumbnail of Asymptotic strong duality

Numerical Algebra, Control and Optimization, 2011

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Research paper thumbnail of Iterative methods for solving stochastic convex feasibility problems and applications

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Research paper thumbnail of Strong duality for generalized monotropic programming in infinite dimensions

Fenchel duality Epigraph of a convex function Conjugate function a b s t r a c t We establish dua... more Fenchel duality Epigraph of a convex function Conjugate function a b s t r a c t We establish duality results for the generalized monotropic programming problem in separated locally convex spaces. We formulate the generalized monotropic programming (GMP) as the minimization of a (possibly infinite) sum of separable proper convex functions, restricted to a closed and convex cone. We obtain strong duality under a constraint qualification based on the closedness of the sum of the epigraphs of the conjugates of the convex functions. When the objective function is the sum of finitely many proper closed convex functions, we consider two types of constraint qualifications, both of which extend those introduced in the literature. The first constraint qualification ensures strong duality, and is equivalent to the one introduced by Boţ and Wanka. The second constraint qualification is an extension of Bertsekas' constraint qualification and we use it to prove zero duality gap.

Bookmarks Related papers MentionsView impact

Research paper thumbnail of The joint EUROPT-OMS conference on optimization, Prague, Czech Republic, July 4–7, 2007, Part I

Optimization Methods and Software

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Research paper thumbnail of The joint EUROPT-OMS conference on optimization, Prague, Czech Republic, July 4–7, 2007. Part II

Optimization Methods and Software

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Research paper thumbnail of On a Modified Subgradient Algorithm for Dual Problems via Sharp Augmented Lagrangian*

Journal of Global Optimization, 2006

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Research paper thumbnail of Generalized proximal point methods for the variational inequality problem

Bookmarks Related papers MentionsView impact

Research paper thumbnail of On primal convergence for augmented Lagrangian duality

Http Dx Doi Org 10 1080 02331934 2010 527971, Aug 1, 2011

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Research paper thumbnail of Corrigendum to: “On a family of convex functions associated to subdifferentials”

Journal of nonlinear and convex analysis

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Research paper thumbnail of Set-valued mappings and enlargement of monotone operators

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Research paper thumbnail of Operating enlargements of monotone operators: new connections with convex functions

Pacific Journal of Mathematics

Given a maximal monotone operator T in a Banach space, a family of enlargements E(T) of T has bee... more Given a maximal monotone operator T in a Banach space, a family of enlargements E(T) of T has been introduced by Svaiter. He also defined a sum and a positive scalar multiplication of enlargements. The first aim of this work is to further study the properties of these operations. Burachik and Svaiter studied a family of convex functions H(T) which is in a one to one correspondence with E(T). The second

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Research paper thumbnail of Set-valued mappings & enlargements of monotone operators

This book is addressed to mathematicians, engineers, economists, and researchers interested in ac... more This book is addressed to mathematicians, engineers, economists, and researchers interested in acquiring a solid mathematical foundation in topics such as point-to-set operators, variational inequalities, general equilibrium theory, and nonsmooth optimization, among others. Containing extensive exercises and examples throughout the text, the first four chapters of the book can also be used for a one-quarter course in set-valued analysis and maximal monotone operators for graduate students in pure and applied mathematics, mathematical economics, operations research and related areas. The only requisites, besides a minimum level of mathematical maturity, are some basic results of general topology and functional analysis.

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Research paper thumbnail of An Additive Subfamily of Enlargements of a Maximally Monotone Operator

Set-Valued and Variational Analysis, 2015

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Research paper thumbnail of Enlargements of Monotone Operators

Optimization and Its Applications, 2008

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Research paper thumbnail of Convex Analysis and Fixed Point Theorems

Optimization and Its Applications, 2008

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Research paper thumbnail of Set Convergence and Point-to-Set Mappings

Optimization and Its Applications, 2008

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Research paper thumbnail of Recent Topics in Proximal Theory

Optimization and Its Applications, 2008

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Research paper thumbnail of ε-Enlargements of Maximal Monotone Operators: Theory and Applications

Applied Optimization, 1998

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Research paper thumbnail of Monotone Operators Without Enlargements

Springer Proceedings in Mathematics & Statistics, 2013

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Research paper thumbnail of A Deflected Subgradient Method Using a General Augmented Lagrangian Duality with Implications on Penalty Methods

Springer Optimization and Its Applications, 2010

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Research paper thumbnail of Asymptotic strong duality

Numerical Algebra, Control and Optimization, 2011

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Research paper thumbnail of Iterative methods for solving stochastic convex feasibility problems and applications

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