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SUMMARY:Generalized Nash Equilibrium Problems with Application to Spot Mar
 kets with Gas Transport - Michael Hintermüller (Weierstraß-Institut für
  Angewandte Analysis und Stochastik\; Humboldt-Universität zu Berlin)
DTSTART:20190321T163000Z
DTEND:20190321T171500Z
UID:TALK121435@talks.cam.ac.uk
CONTACT:INI IT
DESCRIPTION:A class of noncooperative Nash equilibrium problems is present
 ed\, in which the feasible set of each player is perturbed by the decision
 s of their competitors via a convex constraint. In addition\, for every ve
 ctor of decisions\, a common &ldquo\;state&rdquo\; variable is given by th
 e solution of an affine linear equation. The resulting problem is therefor
 e a generalized Nash equilibrium problem (GNEP). The existence of an equil
 ibrium for this problem is demonstrated\, and first-order optimality condi
 tions are derived under a constraint qualification. An approximation schem
 e is proposed\, which involves the solution of a parameter-dependent seque
 nce of standard Nash equilibrium problems. An associated path-following st
 rategy based on the Nikaido&ndash\;Isoda function is then proposed. Functi
 on space- based numerics for parabolic GNEPs and a spot-market model are d
 eveloped.
LOCATION:Seminar Room 1\, Newton Institute
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