Abstract.
We establish existence results for finite dimensional vector minimization problems allowing the solution set to be unbounded. The solutions to be referred are ideal(strong)/weakly efficient(weakly Pareto). Also several necessary and/or sufficient conditions for the solution set to be non-empty and compact are established. Moreover, some characterizations of the non-emptiness (boundedness) of the (convex) solution set in case the solutions are searched in a subset of the real line, are also given. However, the solution set fails to be convex in general. In addition, special attention is addressed when the underlying cone is the non-negative orthant and when the semi-strict quasiconvexity of each component of the vector-valued function is assumed. Our approach is based on the asymptotic description of the functions and sets. Some examples illustrating such an approach are also exhibited.
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Received: February 2000 / Accepted: May 2002 Published online: September 5, 2002
RID="†"
ID="†" Research supported in part by CONICYT-Chile through FONDECYT 101-0116 and FONDAP-Matemáticas Aplicadas II. e-mail: fflores@ing-mat.udec.cl
Key words. convex vector optimization – ideal solution – weakly efficient solution – efficient solution – recession function – recession cone – convex analysis
Mathematics Subject Classification (2000): 90C25, 90C26, 90C29, 90C30, 90C48, 90C99
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Flores-Bazán, F. Ideal, weakly efficient solutions for vector optimization problems. Math. Program., Ser. A 93, 453–475 (2002). https://doi.org/10.1007/s10107-002-0311-4
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DOI: https://doi.org/10.1007/s10107-002-0311-4