Approximate solutions of vector optimization problems via improvement sets in real linear spaces

C. Gutiérrez (), L. Huerga (), B. Jiménez () and V. Novo ()
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C. Gutiérrez: IMUVA (Institute of Mathematics of University of Valladolid)
L. Huerga: Universidad Nacional de Educación a Distancia (UNED)
B. Jiménez: Universidad Nacional de Educación a Distancia (UNED)
V. Novo: Universidad Nacional de Educación a Distancia (UNED)

Journal of Global Optimization, 2018, vol. 70, issue 4, No 9, 875-901

Abstract: Abstract We deal with a constrained vector optimization problem between real linear spaces without assuming any topology and by considering an ordering defined through an improvement set E. We study E-optimal and weak E-optimal solutions and also proper E-optimal solutions in the senses of Benson and Henig. We relate these types of solutions and we characterize them through approximate solutions of scalar optimization problems via linear scalarizations and nearly E-subconvexlikeness assumptions. Moreover, in the particular case when the feasible set is defined by a cone-constraint, we obtain characterizations by means of Lagrange multiplier rules. The use of improvement sets allows us to unify and to extend several notions and results of the literature. Illustrative examples are also given.

Keywords: Vector optimization; Improvement set; Approximate weak efficiency; Approximate proper efficiency; Nearly E-subconvexlikeness; Linear scalarization; Lagrange multipliers; algebraic interior; Vector closure; Primary 90C26; 90C29; Secondary 90C46; 90C48; 49K27 (search for similar items in EconPapers)
Date: 2018
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Citations: View citations in EconPapers (5)

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DOI: 10.1007/s10898-017-0593-y

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