New Generalized Second-Order Contingent Epiderivatives and Set-Valued Optimization Problems
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In this paper, we introduce the concept of a generalized second-order composed contingent epiderivative for set-valued maps and discuss its relationship to the generalized second-order contingent epiderivative. We also investigate some of its properties. Then, by virtue of the generalized second-order composed contingent epiderivative, we establish a unified second-order sufficient and necessary optimality condition for set-valued optimization problems, which is a generalization of the corresponding results in the literature.
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Zhu, S.; Li, S.; Teo, Kok Lay (2013)In this paper, we propose the concept of a second-order composed contingent derivative for set-valued maps, discuss its relationship to the second-order contingent derivative and investigate some of its special properties. ...
Higher-order optimality conditions for weakly efficient solutions in nonconvex set-valued optimizationWang, L.; Li, S.; Teo, Kok Lay (2010)In this paper, generalized higher-order contingent (adjacent) derivatives of set-valued maps are introduced and some of their properties are discussed. Under no any convexity assumptions, necessary and sufficient optimality ...
Wang, Q.; Li, S.; Teo, Kok Lay (2011)In this paper, some properties are established for second-order adjacent derivatives of set-valued maps. Upper and lower semicontinuity and closedness are obtained for second-order adjacent derivatives of weak perturbation ...