Nguyễn Huy Hưng - Academia.edu (original) (raw)
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Papers by Nguyễn Huy Hưng
Applicable Analysis, Jan 18, 2022
This paper deals with approximate solutions of a nonsmooth semi-infinite programming with multipl... more This paper deals with approximate solutions of a nonsmooth semi-infinite programming with multiple interval-valued objective functions. We first introduce four types of approximate quasi Pareto solutions of the considered problem by considering the lower-upper interval order relation and then apply some advanced tools of variational analysis and generalized differentiation to establish necessary optimality conditions for these approximate solutions. Sufficient conditions for approximate quasi Pareto solutions of such a problem are also provided by means of introducing the concepts of approximate (strictly) pseudo-quasi generalized convex functions defined in terms of the limiting subdifferential of locally Lipschitz functions. Finally, a Mond-Weir type dual model in approximate form is formulated, and weak, strong and converse-like duality relations are proposed.
arXiv (Cornell University), Dec 23, 2022
This paper deals with Pareto solutions of a nonsmooth fractional interval-valued multiobjective o... more This paper deals with Pareto solutions of a nonsmooth fractional interval-valued multiobjective optimization. We first introduce four types of Pareto solutions of the considered problem by considering the lower-upper interval order relation and then apply some advanced tools of variational analysis and generalized differentiation to establish necessary optimality conditions for these solutions. Sufficient conditions for Pareto solutions of such a problem are also provided by means of introducing the concepts of (strictly) generalized convex functions defined in terms of the limiting/Mordukhovich subdifferential of locally Lipschitzian functions. Finally, a Mond-Weir type dual model is formulated, and weak, strong and converse-like duality relations are examined.
Applicable Analysis, 2022
This paper deals with approximate solutions of a nonsmooth semi-infinite programming with multipl... more This paper deals with approximate solutions of a nonsmooth semi-infinite programming with multiple interval-valued objective functions. We first introduce four types of approximate quasi Pareto solutions of the considered problem by considering the lower-upper interval order relation and then apply some advanced tools of variational analysis and generalized differentiation to establish necessary optimality conditions for these approximate solutions. Sufficient conditions for approximate quasi Pareto solutions of such a problem are also provided by means of introducing the concepts of approximate (strictly) pseudo-quasi generalized convex functions defined in terms of the limiting subdifferential of locally Lipschitz functions. Finally, a Mond-Weir type dual model in approximate form is formulated, and weak, strong and converse-like duality relations are proposed.
Applicable Analysis, Jan 18, 2022
This paper deals with approximate solutions of a nonsmooth semi-infinite programming with multipl... more This paper deals with approximate solutions of a nonsmooth semi-infinite programming with multiple interval-valued objective functions. We first introduce four types of approximate quasi Pareto solutions of the considered problem by considering the lower-upper interval order relation and then apply some advanced tools of variational analysis and generalized differentiation to establish necessary optimality conditions for these approximate solutions. Sufficient conditions for approximate quasi Pareto solutions of such a problem are also provided by means of introducing the concepts of approximate (strictly) pseudo-quasi generalized convex functions defined in terms of the limiting subdifferential of locally Lipschitz functions. Finally, a Mond-Weir type dual model in approximate form is formulated, and weak, strong and converse-like duality relations are proposed.
arXiv (Cornell University), Dec 23, 2022
This paper deals with Pareto solutions of a nonsmooth fractional interval-valued multiobjective o... more This paper deals with Pareto solutions of a nonsmooth fractional interval-valued multiobjective optimization. We first introduce four types of Pareto solutions of the considered problem by considering the lower-upper interval order relation and then apply some advanced tools of variational analysis and generalized differentiation to establish necessary optimality conditions for these solutions. Sufficient conditions for Pareto solutions of such a problem are also provided by means of introducing the concepts of (strictly) generalized convex functions defined in terms of the limiting/Mordukhovich subdifferential of locally Lipschitzian functions. Finally, a Mond-Weir type dual model is formulated, and weak, strong and converse-like duality relations are examined.
Applicable Analysis, 2022
This paper deals with approximate solutions of a nonsmooth semi-infinite programming with multipl... more This paper deals with approximate solutions of a nonsmooth semi-infinite programming with multiple interval-valued objective functions. We first introduce four types of approximate quasi Pareto solutions of the considered problem by considering the lower-upper interval order relation and then apply some advanced tools of variational analysis and generalized differentiation to establish necessary optimality conditions for these approximate solutions. Sufficient conditions for approximate quasi Pareto solutions of such a problem are also provided by means of introducing the concepts of approximate (strictly) pseudo-quasi generalized convex functions defined in terms of the limiting subdifferential of locally Lipschitz functions. Finally, a Mond-Weir type dual model in approximate form is formulated, and weak, strong and converse-like duality relations are proposed.