On Range Space Techniques, Convex Cones, Polyhedra and Optimization in Infinite Dimensions
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Beschreibung
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.
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.
Illustrates the primary importance the role of range spaces and of the theory of convex cones in optimization Written with the aim to address largest possible audience including not only mathematicians but engineers as well Presents an original range space and conical theory of infinite dimensional polyhedra
Autor*in
Paolo d'Alessandro
Themen in »On Range Space Techniques, Convex Cones, Polyhedra and Optimization in Infinite Dimensions«
Range Spaces Convex Cones Infinite dimensional Linear programming Convex Hypersurfaces
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"The text offers a rigorous and innovative perspective on optimization and convex analysis, aimed at researchers and advanced students interested in functional analysis, control theory, and infinite-dimensional optimization." (Mircea Balaj, Mathematical Reviews, May, 2026)
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