Horizon and Recession Asymptotic Notions for Sets and Mappings: A Unified Approach

Yboon García (), Bruno Goicochea (), Rubén López () and Javier Martínez ()
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Yboon García: Universidad del Pacífico
Bruno Goicochea: Instituto de Matemática y Ciencias Afines (IMCA), Programa de Maestría en Matemática Aplicada
Rubén López: Universidad de Tarapacá
Javier Martínez: Universidad de Tarapacá, Programa de Doctorado en Ciencias con Mención en Matemática

Journal of Optimization Theory and Applications, 2025, vol. 205, issue 2, No 14, 31 pages

Abstract: Abstract The aim of this paper is to develop a unified theory of horizon and recession asymptotic notions for sets, functions, and multifunctions. This unified approach allows to exploit both the algebraic and topological features of these objects. We study the notion of regular set defined as a set for which its horizon and recession cones coincide. This notion plays an important role in the theory. Regular functions and multifunctions are defined and studied as well. By using the unified approach, we obtain properties, formulas, calculus rules, and relationships for horizon and recession notions. Finally, we study the horizon and recession mappings of various important functions and multifunctions from variational analysis.

Keywords: Horizon cone; Horizon mapping; Recession cone; Recession mapping; Regular set; Regular mapping; 26E25; 46N10; 47H04; 49J53; 49K21; 54C60; 90C31; 91B02 (search for similar items in EconPapers)
Date: 2025
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DOI: 10.1007/s10957-025-02655-y

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