ICS »

Stream: Optimal control and applications

Chair: Thomas Weber

1. A smoothing approximation for solving a class of variational inequalities. Application to the strategy based congested transit assignment model
   Esteve Codina, Gemma Ibañez, Lídia Montero
   
   
   

   This paper shows how a given class of variational inequality problems can be solved using a smoothing approximation. Particularly its application to the strategy based user equilibrium transit assignment model is illustrated. The problem can be approximated by a classical smoothing technique leading to another variational inequality model that can be solved by means of a path based method for the asymmetric traffic assignment problem. Computational tests have been carried out on several medium-large scale networks showing the viability and the applicability to large scale transit models.
   
   

2. Decomposition Method for Oligopolistic Competitive Models with a Joint Emission Upper Bound
   Giorgia Oggioni, Elisabetta Allevi, Adriana Gnudi, Igor Konnov
   
   
   

   We consider the general problem of a system of firms subject to common emission upper bounds. Due to these restrictions, the problem is treated as a generalized non-cooperative. We suggest a decomposable share allocation method for attaining the corresponding generalized equilibrium state in a rather natural way. This replaces the initial problem with a sequence of usual non-cooperative games defined on Cartesian product sets. We also show that its implementation can be simplified after application of a regularized penalty method. In the case study, we consider the application of the EU-ETS.
   
   

3. Tangencity to singularity and degenerate optimization problems
   Ewa Bednarczuk, Alexey Tretyakov
   
   
   

   In this talk we present description of the tangent cone in the non-regular. Comparing to the existing results we generalize the concept of p-regularity of mappings and apply this generalization to a wide class of singular problems. We describe tangent cones in these class of mappings and obtain new optimality conditions for such type of optimization problems with equality constraints.
   
   

4. Global Optimization on an Interval
   Thomas Weber
   
   
   

   We provide semi-analytic expressions for the largest and smallest solution of a global optimization problem on an interval using an adjoint variable which represents the available one-sided improvements. The resulting optimality conditions yield two-point boundary problems as in dynamic optimization. We provide several practical examples and consider the challenges of generalizing the method to higher dimensions.