Abstract
In this paper, motivated by a result due to Champion [Math. Program.99, 2004], we introduce a property \({\mathcal{D}(y)}\) for a conic quasi-convex vector-valued function in a general normed space. We prove that this property \({\mathcal{D}(y)}\) 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 \({\mathcal{D}(y).}\)
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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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Ban, L., Song, W. Duality gap of the conic convex constrained optimization problems in normed spaces. Math. Program. 119, 195–214 (2009). https://doi.org/10.1007/s10107-008-0207-z
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DOI: https://doi.org/10.1007/s10107-008-0207-z
Keywords
- Zero duality gap
- Conical-convex constrained optimization
- S-convex mapping
- \({\mathcal{D}(y)}\) property
- Normed spaces