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On range space techniques, convex cones, polyhedra and optimization in infinite dimensions

Record Type:	Electronic resources : Monograph/item
Title/Author:	On range space techniques, convex cones, polyhedra and optimization in infinite dimensionsby Paolo d'Alessandro.
Author:	D'Alessandro, Paolo.
Published:	Cham :Springer Nature Switzerland :2025.
Description:	xi, 475 p. :ill., digital ;24 cm.
Contained By:	Springer Nature eBook
Subject:	Convex programming.
Online resource:	https://doi.org/10.1007/978-3-031-92477-4
ISBN:	9783031924774$q(electronic bk.)

On range space techniques, convex cones, polyhedra and optimization in infinite dimensions
D'Alessandro, Paolo.

On range space techniques, convex cones, polyhedra and optimization in infinite dimensions[electronic resource] /by Paolo d'Alessandro. - Cham :Springer Nature Switzerland :2025. - xi, 475 p. :ill., digital ;24 cm.

Introduction. -- Basic Facts of Set Theory. -- Linear Spaces. -- Rudiments of General Topology. -- Filters: the Fifth Equivalence. -- Hahn Banach andSeparation Theorems. -- Locally Convex and Barrelled Spaces. -- Metrics and pseudometrics, Norms and Pseudonorms. -- Topological Form of Hahn Banach and Separation Theorems. -- Extreme points, Faces, Support and the KreinMilman Theorem. -- Function Spaces.

This book is a research monograph with specialized mathematical preliminaries. It presents an original range space and conic theory of infinite dimensional polyhedra (closed convex sets) and optimization over polyhedra in separable Hilbert spaces, providing, in infinite dimensions, a continuation of the author's book: A Conical Approach to Linear Programming, Scalar and Vector Optimization Problems, Gordon and Breach Science Publishers, Amsterdam, 1997. It expands and improves author's new approach to the Maximum Priciple for norm oprimal control of PDE, based on theory of convex cones, providing shaper results in various Hilbert space and Banach space settings. It provides a theory for convex hypersurfaces in lts and Hilbert spaces. For these purposes, it introduces new results and concepts, like the generalizations to the non compact case of cone capping and of the Krein Milman Theorem, an extended theory of closure of pointed cones, the notion of beacon points, and a necessary and sufficient condition of support for void interior closed convex set (complementing the Bishop Phelps Theorem), based on a new decomposition of non closed non pointed cones with non closed lineality space.

ISBN: 9783031924774$q(electronic bk.)

Standard No.: 10.1007/978-3-031-92477-4doiSubjects--Topical Terms:

185825
Convex programming.

LC Class. No.: QA402.5

Dewey Class. No.: 519.76

On range space techniques, convex cones, polyhedra and optimization in infinite dimensions
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505 0 $a Introduction. -- Basic Facts of Set Theory. -- Linear Spaces. -- Rudiments of General Topology. -- Filters: the Fifth Equivalence. -- Hahn Banach andSeparation Theorems. -- Locally Convex and Barrelled Spaces. -- Metrics and pseudometrics, Norms and Pseudonorms. -- Topological Form of Hahn Banach and Separation Theorems. -- Extreme points, Faces, Support and the KreinMilman Theorem. -- Function Spaces.
520 $a This book is a research monograph with specialized mathematical preliminaries. It presents an original range space and conic theory of infinite dimensional polyhedra (closed convex sets) and optimization over polyhedra in separable Hilbert spaces, providing, in infinite dimensions, a continuation of the author's book: A Conical Approach to Linear Programming, Scalar and Vector Optimization Problems, Gordon and Breach Science Publishers, Amsterdam, 1997. It expands and improves author's new approach to the Maximum Priciple for norm oprimal control of PDE, based on theory of convex cones, providing shaper results in various Hilbert space and Banach space settings. It provides a theory for convex hypersurfaces in lts and Hilbert spaces. For these purposes, it introduces new results and concepts, like the generalizations to the non compact case of cone capping and of the Krein Milman Theorem, an extended theory of closure of pointed cones, the notion of beacon points, and a necessary and sufficient condition of support for void interior closed convex set (complementing the Bishop Phelps Theorem), based on a new decomposition of non closed non pointed cones with non closed lineality space.
650 0 $a Convex programming. $3 185825
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650 1 4 $a Continuous Optimization. $3 558846
650 2 4 $a Optimization. $3 274084
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