Kuhn-Tucker Condition and the Wolfe Duality of Preinvex Set-Valued Optimization
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摘要: 研究了拟不变凸集值优化最优性的Kuhn-Tucker条件及Wolfe型对偶问题.首先引进了alpha-阶G-拟不变凸集和alpha-阶S-拟不变凸集值函数的概念,由此研究了alpha-阶G-拟不变凸集所对应的伴随切锥及alpha-阶伴随导数的性质;最后,借助alpha-阶伴随切导数刻画了alpha-阶S-拟不变凸集值优化最优性的Kuhn-Tucker条件和Wolfe型对偶.Abstract: The optimality Kuhn-Tucker condition and the Wolfe duality for the preinvex set-valued optimization are investigated. Firstly, the concepts of alpha-order G-invex set and the alpha-order S-preinvex set-valued function were introduced, from which the properties of the corresponding contingent cone and the alpha-order contingent derivative were studied; Then, the optimality Kuhn-Tucker condition and the Wolfe duality theorem for the alpha-order S-preinvex set-valued optimization were presented with the help of the alpha-order contingent derivative.
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