Optimality Conditions for Tanaka’s Approximate Solutions in Vector Optimization

César Gutiérrez (), Bienvenido Jiménez () and Vicente Novo ()
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César Gutiérrez: Universidad de Valladolid, Edificio de Tecnologías de la Información y las Telecomunicaciones
Bienvenido Jiménez: Universidad Nacional de Educación a Distancia
Vicente Novo: Universidad Nacional de Educación a Distancia

A chapter in Generalized Convexity and Related Topics, 2007, pp 279-295 from Springer

Abstract: Summary In this work, approximate solutions of vector optimization problems in the sense of Tanaka [18] are characterized via scalarization. Necessary and sufficient conditions are obtained using a new order representing property and a new monotonicity concept, respectively. A family of gauge functions defined by generalized Chebyshev norms and verifying both properties is introduced in order to characterize approximate solutions of vector optimization problems via approximate solutions of several scalarizations.

Keywords: Vector optimization; ε-efficient solutions; scalarization; gauge function; generalized Chebyshev norms (search for similar items in EconPapers)
Date: 2007
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DOI: 10.1007/978-3-540-37007-9_16

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