**Optimality conditions and duality for multiobjective ****optimization with equilibrium constraints in terms of Michel-Penot ****subdifferentials**

Lê Thanh Tùng (Cần Thơ Univ.)

20.09.2020 - 09h30

Room B.43

*Abstract*: In this paper, we consider nonsmooth multiobjective optimization problems with equilibrium constraints. By using Michel-Penot subdifferential, we first establish necessary conditions and sufficient conditions for optimality. Then, we propose a Wolfe-type and a Mond-Weir-type of dual problems and explore duality relations under generalized convexity assumptions. Some examples are provided to illustrate our results.

**Stability of a solution map to a vector equilibrium problem via an oriented distance function and applications**

Phạm Thanh Dược (Võ Trường Toản Univ.)

24.05.2020 - 09h30

Room F.305

*Abstract*: In this talk, we consider strong vector equilibrium problems in normed spaces. Firstly, we consider stability conditions for the scalar equilibrium problem without assuming concavity properties of the objective function. Next, we use the oriented distance function to study stability conditions of an approximate solution map to the strong vector equilibrium problem via the corresponding one for the scalar model. As an application, we apply the obtained results to formulate the stability for network equilibrium problems.

**Lagrange Multiplier Rules in Nonsmooth Robust Multiobjective Semi-Infinite Optimization Problems**

Nguyễn Minh Tùng

22.12.2019 - 09h30

Room B.37

*Abstract*: In this talk, we consider a robust nonsmooth semi-infinite multiobjective optimization problem with uncertain data in terms of Clarke's subdifferential of locally Lipschitz functions. We propose some robust constraint qualifications. Then, we apply them to obtain some robust necessary optimality conditions for important robust solutions in the sense of weak Pareto, proper, and isolated solutions. Our conditions are Karush-Kuhn-Tucker multiplier rules. Besides, we also investigate the boundedness of these multiplier sets. Further, robust sufficient optimality conditions for these solutions are also derived under generalized convexity assumptions. Finally, some characterizations of solutions are formulated via a gap function associated with the given problem.

**Karush-Kuhn-Tucker optimality conditions and duality for Lipschitz semi-infinite programming with multiple interval-valued objective functions**

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TS. Lê Thanh Tùng (Cần Thơ Univ.)

24.11.2019 - 09h30

Room F.302

*Abstract*: This talk deals with Lipschitz semi-infinite programming with multiple interval-valued objective functions. We first investigate necessary and sufficient Karush-Kuhn-Tucker optimality conditions for some types of optimal solutions. Then, we formulate types of Mond-Weir and Wolfe dual problems and explore duality relations under convexity assumptions. Some examples are provided to illustrate the advantages of our results in some cases.

**Stability of Efficient Solutions to Set Optimization Problems**

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Đinh Vinh Hiển (Univ. of Food Industry)

27.10.2019 - 09h30

Room F302

*Abstract*: In this talk, we focus our attention on stability of efficient solutions to set optimization problems. First, we introduce the concepts of set optimization problems and their solutions based on set less order relations in the image space. Next, the external and internal stability of efficient solutions to such problems are investigated. Namely, limit of a converging net of efficient solutions to perturbed problems is a solution to the original problem. Conversely, any given solution to the original problem, we can express it as a limit of a net of efficient solutions to perturbed problems. Our results are new or improve the existing ones in the litterature.

General versions of the Ekeland variational principle and the Simon satisficing principle.Lê Phước Hải
02.06.2019 - 09h30
Room F.304
Abstract: We prove new general versions of the Ekeland variational principle in a partial quasi-metric space. Unlike the existing versions of this principle, besides a perturbation in terms of the partial quasi-metric, another perturbation being a distance-like bifunction is involved. The classical assumptions on lower semicontinuity of the function and completeness of the space are slightly weakened. The proof technique is new, based onshowing the existence of so-called Ekeland points, which are defined through these two perturbations. Then, we show how these new versions provide striking models for satisficing processes where agents, at each period, do not optimize, but, instead, searchand satisfice. Our new versions of the Ekeland variational principle then are used to develop the Simon satisficing principle which advocates that agents set a satisficing threshold level and search for an alternative until it exceeds this given threshold level. Using a recent variational rationality approach of human dynamics, these new versionsof the Ekeland vatiational principle show the existence of variational traps, such that, starting from an initial position, an agent can satisfice in a worthwhile way, and, being there, is unable to satisfice again in a worthwhile way, giving the end of satisficing process. Moreover, the variatonal approach shows that the Ekeland points represent variational traps (at the intersection of two remarkable sets), which appear to be a set of worthwhile moves starting from the initial point and a set of potential ends (stationary traps). |