Regina Burachik - Academia.edu (original) (raw)
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Papers by Regina Burachik
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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Optimization Methods and Software
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Optimization Methods and Software
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Journal of Global Optimization, 2006
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Http Dx Doi Org 10 1080 02331934 2010 527971, Aug 1, 2011
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Journal of nonlinear and convex analysis
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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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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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Set-Valued and Variational Analysis, 2015
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Optimization and Its Applications, 2008
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Optimization and Its Applications, 2008
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Optimization and Its Applications, 2008
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Optimization and Its Applications, 2008
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Applied Optimization, 1998
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Springer Proceedings in Mathematics & Statistics, 2013
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Springer Optimization and Its Applications, 2010
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Numerical Algebra, Control and Optimization, 2011
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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
Optimization Methods and Software
Bookmarks Related papers MentionsView impact
Optimization Methods and Software
Bookmarks Related papers MentionsView impact
Journal of Global Optimization, 2006
Bookmarks Related papers MentionsView impact
Bookmarks Related papers MentionsView impact
Http Dx Doi Org 10 1080 02331934 2010 527971, Aug 1, 2011
Bookmarks Related papers MentionsView impact
Journal of nonlinear and convex analysis
Bookmarks Related papers MentionsView impact
Bookmarks Related papers MentionsView impact
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
Bookmarks Related papers MentionsView impact
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.
Bookmarks Related papers MentionsView impact
Set-Valued and Variational Analysis, 2015
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Optimization and Its Applications, 2008
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Optimization and Its Applications, 2008
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Optimization and Its Applications, 2008
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Optimization and Its Applications, 2008
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Applied Optimization, 1998
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Springer Proceedings in Mathematics & Statistics, 2013
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Springer Optimization and Its Applications, 2010
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Numerical Algebra, Control and Optimization, 2011
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