Invited Session Wed.2.H 2051

Wednesday, 13:15 - 14:45 h, Room: H 2051

Cluster 24: Variational analysis [...]

Equilibrium problems: Formulations and methodologies


Chair: Patrizia Daniele



Wednesday, 13:15 - 13:40 h, Room: H 2051, Talk 1

Patrizia Daniele
General financial models: Methodologies and suggestions for the recovery


We present a general time-dependent equilibrium model of financial flows and prices, obtaining the equilibrium conditions and the governing variational inequality formulation. Using delicate tools of Nonlinear Analysis and especially some properties of the dual model (the so called shadow problem), the optimal composition of assets, liabilities and prices is determined and a qualitative analysis of the equilibrium is performed.



Wednesday, 13:45 - 14:10 h, Room: H 2051, Talk 2

Giovanni Paolo Crespi
Minty variational principle in set optimization

Coauthors: Andreas H. Hamel, Carola Schrage


In scalar optimization it is well known that a solution of a Minty variational inequality of differential type is a solution of the primitive optimization problem. This relation is known as “Minty variational principle.” In the vector case, the links between Minty variational inequalities and vector optimization problems were deeply investigated in the last decades. In the field of vector optimization some convexity assumptions are needed to state the result. We aim to extend such results to set optimization, using suitable notions of solution to the optimization problem and a new approach to the definition of a differential type variational inequality associated to a set-valued function. To this extent a Dini type derivative for a of class set-valued functions will be introduced, convexity and monotonicity will be discussed by means of suitable scalarization techniques. The concepts of infimum in set optimization and non dominated elements will be investigated.



Wednesday, 14:15 - 14:40 h, Room: H 2051, Talk 3

Tina Wakolbinger
A variational inequality formulation of economic network equilibrium models with nonlinear constraints

Coauthors: Patrizia Daniele, Fuminori Toyasaki


Variational inequality theory facilitates the formulation of equilibrium problems in economic networks. Examples of successful applications include models of supply chains, financial networks, transportation networks, and electricity networks. Previous economic network equilibrium models that were formulated as variational inequalities only included linear constraints. In this paper, we first highlight with an application from the context of reverse logistics why the introduction of nonlinear constraints is beneficial. We then show mathematical conditions that ensure that the models have unique solutions and we suggest algorithms that can be applied to solve the models


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