Algorithms for Quasi-Variational Inequalities in Infinite-Dimensional Spaces

Description

The aim of this project is to develop and analyse algorithms for the numerical solution of some classes of quasi-variational inequalities. Such inequalities occur, e.g., in connection with generalized Nash equilibria in multi-player control problems. Moreover, they are widely used to describe the value function in stochastic control problems. Our goal is twofold: a) Transfer existing solution methods from finite-dimensional to infinite-dimensional problems. b) Develop problem-tailored solution methods by taking into account the particular structure of certain quasi-variational inequalities. All methods should have a strong theoretical background and will be tested extensively on suitable examples.

Publications

Christian Kanzow, Daniel Steck: Augmented Lagrangian Methods for the Solution of Generalized Nash Equilibrium Problems, SIAM Journal on Optimization 26 (4), 2016 Christian Kanzow, Daniel Steck: A Generalized Proximal-Point Method for Convex Optimization Problems in Hilbert Spaces , A Journal of Mathematical Programming and Operations Research , 2017 Christian Kanzow, Daniel Steck: An Example Comparing the Standard and Modified Augmented Lagrangian Methods, Operations Research Letters , 2017

Preprints

Christian Kanzow, Daniel Steck: Improved Local Convergence Results for Augmented Lagrangian Methods in $C^2$-Cone Reducible Constrained Optimization (SPP1962-040, 11/2017, [bib])

Christian Kanzow, Daniel Steck: On Error Bounds and Multiplier Methods for Variational Problems in Banach Spaces (SPP1962-034, 09/2017, [bib])

Christian Kanzow, Daniel Steck, Veronika Karl, Daniel Wachsmuth: The Multiplier-Penalty Method for Generalized Nash Equilibrium Problems in Banach Spaces (SPP1962-028, 07/2017, [bib])

Veronika Karl, Frank Pörner: An Augmented Lagrange Method for Ill-Posed Elliptic State Constrained Optimal Control Problems with Sparse Controls (SPP1962-027, 07/2017, [bib])

Christian Kanzow, Daniel Steck: An Example Comparing the Standard and Modified Augmented Lagrangian Methods (SPP1962-013, 03/2017, [bib])

Veronika Karl, Daniel Wachsmuth: An Augmented Lagrange Method for Elliptic State Constrained Optimal Control Problems (SPP1962-008, 02/2017, [bib])

Christian Kanzow, Daniel Steck, Daniel Wachsmuth: An Augmented Lagrangian Method for Optimization Problems in Banach Spaces (SPP1962-003, 12/2016, [bib])

Christian Kanzow, Daniel Steck: A Generalized Proximal-Point Method for Convex Optimization Problems in Hilbert Spaces (SPP1962-002, 12/2016, [bib])

Research Area

Members

  • member's portrait

    Prof. Christian Kanzow

    Julius-Maximilians-Universität Würzburg
    Principal Investigator
  • member's portrait

    Prof. Daniel Wachsmuth

    Julius-Maximilians-Universität Würzburg
    Principal Investigator
  • member's portrait

    Veronika Karl

    Julius-Maximilians-Universität Würzburg
    Research Assistant
  • member's portrait

    Daniel Steck

    Julius-Maximilians-Universität Würzburg
    Research Assistant

Project Related News

  • 17. 02. 2017 : Welcome to our new project member

    Veronika Karl joins project 14.