Karush–Kuhn–Tucker Multiplier Rules for Efficient Solutions of Set-Valued Equilibrium Problem with Constraints

Author(s):  
Nguyen Minh Tung
Complexity ◽  
2020 ◽  
Vol 2020 ◽  
pp. 1-7
Author(s):  
Yameng Zhang ◽  
Guolin Yu ◽  
Wenyan Han

This paper is devoted to the investigation of optimality conditions for approximate quasi weak efficient solutions for a class of vector equilibrium problem (VEP). First, a necessary optimality condition for approximate quasi weak efficient solutions to VEP is established by utilizing the separation theorem with respect to the quasirelative interior of convex sets and the properties of the Clarke subdifferential. Second, the concept of approximate pseudoconvex function is introduced and its existence is verified by a concrete example. Under the assumption of introduced convexity, a sufficient optimality condition for VEP in sense of approximate quasi weak efficiency is also presented. Finally, by using Tammer’s function and the directed distance function, the scalarization theorems of the approximate quasi weak efficient solutions of the VEP are proposed.


2012 ◽  
Vol 62 (1) ◽  
Author(s):  
Qing-You Liu ◽  
Xian-Jun Long ◽  
Nan-jing Huang

AbstractIn this paper, a generalized vector equilibrium problem is introduced and studied. A scalar characterization of weak efficient solutions for the generalized vector equilibrium problem is obtained. By using the scalarization result, the existence of the weak efficient solutions and the connectedness of the set of weak efficient solutions for the generalized vector equilibrium problem are proved in locally convex spaces.


2010 ◽  
Vol 12 (1) ◽  
pp. 51-59
Author(s):  
Yanhong HU ◽  
Wen SONG
Keyword(s):  

2020 ◽  
Vol 27 (38) ◽  
pp. 6523-6535 ◽  
Author(s):  
Antreas Afantitis ◽  
Andreas Tsoumanis ◽  
Georgia Melagraki

Drug discovery as well as (nano)material design projects demand the in silico analysis of large datasets of compounds with their corresponding properties/activities, as well as the retrieval and virtual screening of more structures in an effort to identify new potent hits. This is a demanding procedure for which various tools must be combined with different input and output formats. To automate the data analysis required we have developed the necessary tools to facilitate a variety of important tasks to construct workflows that will simplify the handling, processing and modeling of cheminformatics data and will provide time and cost efficient solutions, reproducible and easier to maintain. We therefore develop and present a toolbox of >25 processing modules, Enalos+ nodes, that provide very useful operations within KNIME platform for users interested in the nanoinformatics and cheminformatics analysis of chemical and biological data. With a user-friendly interface, Enalos+ Nodes provide a broad range of important functionalities including data mining and retrieval from large available databases and tools for robust and predictive model development and validation. Enalos+ Nodes are available through KNIME as add-ins and offer valuable tools for extracting useful information and analyzing experimental and virtual screening results in a chem- or nano- informatics framework. On top of that, in an effort to: (i) allow big data analysis through Enalos+ KNIME nodes, (ii) accelerate time demanding computations performed within Enalos+ KNIME nodes and (iii) propose new time and cost efficient nodes integrated within Enalos+ toolbox we have investigated and verified the advantage of GPU calculations within the Enalos+ nodes. Demonstration data sets, tutorial and educational videos allow the user to easily apprehend the functions of the nodes that can be applied for in silico analysis of data.


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