Abstract
In this paper, duality is studied as a consequence of separating certain derived sets related to optimization problems. The interior and convexity conditions used and two groups of related derived sets are studied and a new interior condition for duality arises quite naturally. Several dual problems are presented and the paper is concluded by presentation of saddlepoint optimality criteria for the problems considered.
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References
D.G. Luenberger,Optimization by vector space methods (Wiley, New York, 1969).
D.A. Pyne, “On interior and convexity conditions, development of dual criteria in abstract mathematical programming”, Tech. Rept. No. 175, Department of Mathematical Sciences, The Johns Hopkins University, Baltimore, Md. (1973).
V.A. Sposito and H.T. David, “Saddlepoint optimality criteria of nonlinear programming problems over cones without differentiability”,SIAM Journal on Applied Mathematics 20 (1971) 698–702.
R.M. Van Slyke and R.J.-B. Wets, “A duality theory for abstract programs with applications to optimal control theory”,Journal of Mathematical Applications and Analysis 22 (1968) 679–706.
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Pyne, D.A. On interior and convexity conditions, development of dual problems and saddlepoint optimality criteria in abstract mathematical programming. Mathematical Programming 8, 125–133 (1975). https://doi.org/10.1007/BF01580438
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DOI: https://doi.org/10.1007/BF01580438