Speaker: Dr. Shipra Singh, Post-doctoral Researcher, Technion-Israel Institute of Technology, Haifa, Israel.
Day, Date and Time: Wednesday, 22nd July 2020, 10.30 AM.
Title of the Talk: Study of variational inequality problems with their applications in optimization and real world problems.
Abstract:
The conception of variational inequality problem was originated by the calculus of variations associated with the minimization of infinite dimensional functionals. A classical variational inequality problem is an inequality comprising a functional, which has to be investigated for all possible values of a given variable, belonging usually to a convex set. Indeed, a variational inequality is very closely related to many mathematical problems, such as complementarity problem, Nash equilibrium problem, system of equations, optimization problem and fixed point problem. These mathematical problems can be formulated as a variational inequality or in other way, we can say that these are the special cases of a variational inequality problem. On the other hand, several problems related to economic world, for instance, traffic network equilibrium problems, spatial price equilibrium problems, oligopolistic market equilibrium problems, migration equilibrium problems etc. can be transformed into a variational inequality problem.
More specifically, this talk will be focused on the study of optimization problems and traffic network problems via variational inequality problems. Firstly, I will give a brief description of some important types of variational inequality problems and their uses in the study of different kinds of optimization problems as well. Thereafter, I will give a brief demonstration on the study of traffic network problems in the terms of a variational inequality problem.
Speaker Bio:
Dr. Shipra Singh recently started to work as a postdoctoral researcher at the Technion-Israel Institute of Technology, Haifa Israel. Before this, Dr. Shipra Singh was working as a postdoctoral researcher at the University of Electronic Science and Technology of China from April 2018 to March 2020. She completed her PhD from Indian Institute of Technology (Indian School of Mines) Dhanbad. The main thrust of her research interest is the study of variational inequality problems and their applications in optimization and real world problems. Her research is influenced by a variety of factors of optimization such as optimal control problems, convex optimization and mathematical modelling. During Phd and postdoctoral works, she explored several kinds of variational inequality problems in ensuring the existence of efficient and generalized efficient solutions of vector optimization problems, and investigated weak sharp solution concept and iterative methods for solving multitime-dependent and split variational inequality problems together with their importance in multidimensional optimization problems and split inverse problems, respectively. Her ongoing research is focused on the construction of the mathematical models in terms of different kinds of variational inequality problems for the economic world related problems such as traffic network equilibrium problem, electricity spot market problem, spatial price equilibrium problem, oligopolistic market equilibrium problem, financial equilibrium problem and pollution control problem. Among these, her current focus is on traffic network problems and the rest are her future goals.
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