Optimal insider control of stochastic partial differential equations,with applications to optimal harvesting and optimal insider portfolio under noisy observations (ORCOS Seminar)
by Prof. Bernt Øksendal (Department of Mathematics, University of Oslo)
Date: 9th May 2017 - Time: 16:30 - 18:00
Location: seminar room (DB gelb 04)
wing B (yellow area), 4th floor
Wiedner Hauptstraße 8
We study the problem of optimal control with inside information of an SPDE (a stochastic evolution equation) driven by a Brownian motion and a Poisson random measure. Our optimal control problem is new in two ways:
(i) The controller has access to inside information, i.e. access to information about a future state of the system,
(ii) The integro-differential operator of the SPDE might depend on the control.
In the first part of the paper, we formulate a sufficient and a necessary maximum principle for this type of control problem, in the following two cases:
(a) The control is allowed to depend both on time t and on the space variable x.
(b) The control is not allowed to depend on x.
In the second part of the paper, we apply the results above to the problem of optimal control of an SDE system when the inside controller has only noisy observations of the state of the system. Using results from nonlinear filtering, we transform this noisy observation SDE inside control problem into a full observation SPDE insider control problem. The results are illustrated by explicit examples.
The presentation is based on joint works with Olfa Draouil, University of Tunis El Manar, Tunisia.
Exact Methods for Non-Hamiltonian Routing Problems (ISOR Colloquium)
by Hande Yaman (Bilkent Univ.)
Date: 29th May 2017 - Time: 16:45 - 17:45
Location: Hörsaal 7
Faculty of Business, Economics and Statistics
(Oskar-Morgenstern-Platz 1, 1090 Vienna)
The classical traveling salesman problem (TSP) seeks a Hamitonian cycle (a cycle that visits every node exactly once) of minimum cost. Even though early routing problems focus on finding Hamiltonian cycles, many routing applications also require the choice of nodes that are to be visited or the number of times a node is visited. In this talk, we present exact methods for three non-Hamiltonian routing problems; namely, the split delivery VRP, the time constrained maximal covering TSP and the VRP with roaming delivery locations. We propose an iterative approach to solve the split delivery VRP where a relaxation is tigthened at each iteration by adding new variables and constraints. For the time constrained maximal covering TSP, we give a new family of facet defining inequalities and use them in a branch-and-cut approach. Finally, we present a branch-and-price algorithm to solve the VRP with roaming delivery locations. This is joint work with O.E. Karasan, M. Savelsbergh and G. Ozbaygin.