Friday, 11:10 - 12:30 - Room 108

*Stream: Optimal control and applications*

Chair:

- A smoothing approximation for solving a class of variational inequalities. Application to the strategy based congested transit assignment model

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.

- Decomposition Method for Oligopolistic Competitive Models with a Joint Emission Upper Bound

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.

- Tangencity to singularity and degenerate optimization problems

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.

- Global Optimization on an Interval

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.