Duality related to approximate proper solutions of vector optimization problems

C. Gutiérrez (), L. Huerga (), V. Novo () and C. Tammer ()

Journal of Global Optimization, 2016, vol. 64, issue 1, 117-139

Abstract: In this work we introduce two approximate duality approaches for vector optimization problems. The first one by means of approximate solutions of a scalar Lagrangian, and the second one by considering $$(C,\varepsilon )$$ ( C , ε ) -proper efficient solutions of a recently introduced set-valued vector Lagrangian. In both approaches we obtain weak and strong duality results for $$(C,\varepsilon )$$ ( C , ε ) -proper efficient solutions of the primal problem, under generalized convexity assumptions. Due to the suitable limit behaviour of the $$(C,\varepsilon )$$ ( C , ε ) -proper efficient solutions when the error $$\varepsilon $$ ε tends to zero, the obtained duality results extend and improve several others in the literature. Copyright Springer Science+Business Media New York 2016

Keywords: Vector optimization; Approximate duality; Proper $$\varepsilon $$ ε -efficiency; Nearly cone-subconvexlikeness; Linear scalarization; 90C48; 90C25; 90C46; 49N15 (search for similar items in EconPapers)
Date: 2016
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DOI: 10.1007/s10898-015-0366-4

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