15th EUROPT Workshop on Advances in Continuous Optimization

Montréal, Canada, July 12 — 14, 2017

15th EUROPT Workshop on Advances in Continuous Optimization

Montréal, Canada, July 12 — 14, 2017

Schedule Authors My Schedule
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Variational Problems and Applications I

Jul 13, 2017 11:30 AM – 12:45 PM

Location: PWC

Chaired by Giancarlo Bigi

3 Presentations

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    11:30 AM - 11:55 AM

    Bifurcations in Two-Player Nonlinear Games Using Nonsmooth Dynamics and Variational Inequalities

    • Monica-Gabriela Cojocaru, presenter, Dept. Mathematics, University of Guelph

    It is known that Nash equilibrium points of a nonlinear 2-player game can be obtained by the equivalent reformulation of such a game into a variational inequality problem. In this work, we consider the case of a parameter being introduced in one or both of the players' payoffs. In this case the equivalent variational inequality problem becomes dependent on the payoffs' parameters. Furthermore the dynamics naturally associated to such a VI problem becomes a nonsmooth dynamical system whose right hand side will depend on the payoffs' parameter. Thus we are able to ask the question of whether bifurcations of the associated projected system take place, and what is the meaning of these bifurcations for the initial 2-player game. Once more Nash equilibria are established, the persistence and selection questions become pertinent for this set. We present our answers in this talk.

  • Cal add eabad1550a3cf3ed9646c36511a21a854fcb401e3247c61aefa77286b00fe402
    11:55 AM - 12:20 PM

    A variational inequality model for evaluating the security of supply in a natural gas supply chain

    • Giorgia Oggioni, presenter, Department of Economics and Management, University of Brescia, Italy
    • Elisabetta Allevi, University of Brescia
    • Luigi Boffino, Department of Management, Economics and Quantitative Methods, University of Bergamo, Italy
    • Maria Elena De Giuli, Department of Economics and Management, University of Pavia, Italy

    A large part of the European natural gas imports originates from unstable regions exposed to the risk of supply failure due to economical and political reasons. This has increased the concerns on the security of external supply in the European natural gas market. In this paper, we analyze the security of the external supply of the Italian gas market that mainly relies on imports to satisfy its gas demand. In particular, we develop a variational inequality model that describes the equilibrium state of a natural gas supply chain where producers, mid-streamers and consumers are exposed to this supply risk.

  • Cal add eabad1550a3cf3ed9646c36511a21a854fcb401e3247c61aefa77286b00fe402
    12:20 PM - 12:45 PM

    Generalized Nash equilibria and semi-infinite programming

    • Giancarlo Bigi, presenter, University of Pisa, Italy
    • Simone Sagratella, Sapienza Università di Roma

    Bilevel optimization, noncooperative games and semi-infinite programming share some similarities, which may lead to meaningful connections. Indeed, theoretical developments and algorithms developed for one of these models could be exploited to cope with the others. In this talk we focus on the relationships between generalized Nash games and semi-infinite programming. In particular, we show how generalized Nash games can be exploited to solve semi-infinite programs, relying on penalization techniques, nonsmooth optimization and a sequence of suitable saddlepoint problems.

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