joint work with Tan Cao, Giovanni Colombo, Boris Mordukhovich
The talk is devoted to a class of optimal control problems governed by a perturbed sweeping (Moreau) process with the moving convex polyhedral set, where the controls are used to determine the best shape of the moving set in order to optimize the given Bolza-type problem. Using the method of discrete approximations together with the advanced tools of variational analysis and generalized differentiation allows us to efficiently derive the necessary optimality conditions for the discretized control problems and the original controlled problem. Some numerical examples are presented.
joint work with Saverio Bolognani, Gabriela Hug, Florian Dörfler
Autonomous optimization is an emerging concept in control theory that refers to the design of feedback controllers that steer a physical system to a steady state that solves a predefined nonlinear optimization problem. These controllers are modelled after optimization algorithms, but are implemented in closed loop with the physical system. For this interconnection to be stable, both systems need act on sufficiently different timescales. We quantify the required timescale separation and give prescriptions that can be directly used in the design of such feedback-based optimization schemes.
joint work with Christian Bayer, Juho Häppölä
We consider the pricing American basket options in a multivariate setting, including the Black-Scholes, Heston and the rough Bergomi model. In high dimensions, nonlinear PDEs methods for solving the problem become prohibitively costly due to the curse of dimensionality. We propose a stopping rule depending on a low-dimensional Markovian projection of the given basket of assets. We approximate the optimal early-exercise boundary of the option by solving a Hamilton-Jacobi-Bellman PDE in the projected, low-dimensional space. This is used to produce an exercise strategy for the original option.