Friday, 11:10 - 12:30 - Room 108
Stream: Optimal control and applications
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.
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.
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.
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.