Duality gap of the conic convex constrained optimization problems in normed spaces |
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Authors: | Liqun Ban Wen Song |
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Affiliation: | (1) Department of Mathematics, Harbin University of Science and Technology, Harbin, 150080, China;(2) Department of Mathematics, Harbin Normal University, Harbin, 150080, China |
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Abstract: | In this paper, motivated by a result due to Champion [Math. Program.99, 2004], we introduce a property for a conic quasi-convex vector-valued function in a general normed space. We prove that this property characterizes the zero duality gap for a class of the conic convex constrained optimization problem in the sense that if this property is satisfied and the objective function f is continuous at some feasible point, then the duality gap is zero, and if this property is not satisfied, then there exists a linear continuous function f such that the duality gap is positive. We also present some sufficient conditions for the property The work of this author was partially supported by the National Natural Sciences Grant (No. 10671050) and the Excellent Young Teachers Program of MOE, P.R.C. |
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Keywords: | Zero duality gap Conical-convex constrained optimization S-convex mapping IEq4" > /content/h78182105711242g/10107_2008_207_Article_IEq4.gif" alt=" $${mathcal{D}(y)}$$" align=" middle" border=" 0" > property Normed spaces |
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