The Experts below are selected from a list of 24981 Experts worldwide ranked by ideXlab platform
M. Ruiz Galán - One of the best experts on this subject based on the ideXlab platform.
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Revisiting the Hahn–Banach Theorem and nonlinear infinite programming
Journal of Mathematical Analysis and Applications, 2017Co-Authors: P. Montiel López, M. Ruiz GalánAbstract:Abstract The aim of this paper is to state a sharp version of the Konig supremum Theorem, an equivalent reformulation of the Hahn–Banach Theorem. We apply it to derive statements of the Lagrange multipliers, Karush–Kuhn–Tucker and Fritz John types, for nonlinear infinite programs. We also show that a weak concept of convexity coming from minimax theory, infsup-convexity, is the adequate one for this kind of results.
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Revisiting the Hahn-Banach Theorem and Nonlinear Infinite Programming
arXiv: Functional Analysis, 2016Co-Authors: P. Montiel López, M. Ruiz GalánAbstract:[REVISED VERSION] The aim of this paper is to state a sharp version of the K\"onig supremum Theorem, an equivalent reformulation of the Hahn--Banach Theorem. We apply it to derive statements of the Lagrange multipliers, Karush-Kuhn-Tucker and Fritz John type, for nonlinear infinite programs. We also show that a weak concept of convexity coming from minimax theory, infsup-convexity, is the adequate one for this kind of results.
Gertrud Bauer - One of the best experts on this subject based on the ideXlab platform.
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The Hahn-Banach Theorem for Real Vector Spaces
2016Co-Authors: Gertrud BauerAbstract:The Hahn-Banach Theorem is one of the most fundamental results in functional analysis. We present a fully formal proof of two versions of the Theorem, one for general linear spaces and another for normed spaces. This development is based on simply-typed classical set-theory, as provided by Isabelle/HOL.
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TYPES - Computer-Assisted Mathematics at Work (The Hahn-Banach Theorem in Isabelle/Isar)
Lecture Notes in Computer Science, 2000Co-Authors: Gertrud Bauer, Markus WenzelAbstract:We present a complete formalization of the Hahn-Banach Theorem in the simply-typed set-theory of Isabelle/HOL, such that both the modeling of the underlying mathematical notions and the full proofs are intelligible to human readers. This is achieved by means of the Isar environment, which provides a framework for high-level reasoning based on natural deduction. The final result is presented as a readable formal proof document, following usual presentations in mathematical textbooks quite closely. Our case study demonstrates that Isabelle/Isar is capable to support this kind of application of formal logic very well, while being open for an even larger scope.
Markus Wenzel - One of the best experts on this subject based on the ideXlab platform.
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TYPES - Computer-Assisted Mathematics at Work (The Hahn-Banach Theorem in Isabelle/Isar)
Lecture Notes in Computer Science, 2000Co-Authors: Gertrud Bauer, Markus WenzelAbstract:We present a complete formalization of the Hahn-Banach Theorem in the simply-typed set-theory of Isabelle/HOL, such that both the modeling of the underlying mathematical notions and the full proofs are intelligible to human readers. This is achieved by means of the Isar environment, which provides a framework for high-level reasoning based on natural deduction. The final result is presented as a readable formal proof document, following usual presentations in mathematical textbooks quite closely. Our case study demonstrates that Isabelle/Isar is capable to support this kind of application of formal logic very well, while being open for an even larger scope.
P. Montiel López - One of the best experts on this subject based on the ideXlab platform.
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Revisiting the Hahn–Banach Theorem and nonlinear infinite programming
Journal of Mathematical Analysis and Applications, 2017Co-Authors: P. Montiel López, M. Ruiz GalánAbstract:Abstract The aim of this paper is to state a sharp version of the Konig supremum Theorem, an equivalent reformulation of the Hahn–Banach Theorem. We apply it to derive statements of the Lagrange multipliers, Karush–Kuhn–Tucker and Fritz John types, for nonlinear infinite programs. We also show that a weak concept of convexity coming from minimax theory, infsup-convexity, is the adequate one for this kind of results.
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Revisiting the Hahn-Banach Theorem and Nonlinear Infinite Programming
arXiv: Functional Analysis, 2016Co-Authors: P. Montiel López, M. Ruiz GalánAbstract:[REVISED VERSION] The aim of this paper is to state a sharp version of the K\"onig supremum Theorem, an equivalent reformulation of the Hahn--Banach Theorem. We apply it to derive statements of the Lagrange multipliers, Karush-Kuhn-Tucker and Fritz John type, for nonlinear infinite programs. We also show that a weak concept of convexity coming from minimax theory, infsup-convexity, is the adequate one for this kind of results.
Abdullah Aydin - One of the best experts on this subject based on the ideXlab platform.
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hahn banach Theorem for operators on lattice normed riesz algebras
Muş Alparslan Üniversitesi Fen Bilimleri Dergisi, 2020Co-Authors: Abdullah AydinAbstract:X ve E Riesz cebirleri ve p:X →E_+ monoton bir vektor normu olsun. Boylece (X,p,E) uclusu kafes normlu Riesz cebiri olarak adlandirilir. Bu calismada, Hahn-Banach teoreminin kafes normlu Riesz cebirlerindeki operatorler icin genisletilmesini verecegiz. Fakat bu calismadaki genisleme diger Hahn-Banach teoremlerinden farli olmaktadir. Ayrica bu genislemenin bazi sonuclarinin oldugunu gostermeketeyiz.
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hahn banach Theorem for operators on the lattice normed f algebras
arXiv: Functional Analysis, 2020Co-Authors: Abdullah AydinAbstract:Let $X$ and $E$ be $f$-algebras and $p:X \to E_+$ be a monotone vector norm. Then the triple $(X,p,E)$ is called a lattice-normed $f$-algebraic space. In this paper, we show a generalization of the extension of the Hahn-Banach Theorem for operators on the lattice-normed $f$-algebras, in which the extension of one step of that is not similar to the other Hahn-Banach Theorems. Also, we give some applications and results.
