TITLE:
On Optimal Sparse-Control Problems Governed by Jump-Diffusion Processes
AUTHORS:
Beatrice Gaviraghi, Andreas Schindele, Mario Annunziato, Alfio Borzì
KEYWORDS:
Jump-Diffusion Processes, Partial Integro-Differential Fokker-Planck Equation, Optimal Control Theory, Nonsmooth Optimization, Proximal Methods
JOURNAL NAME:
Applied Mathematics,
Vol.7 No.16,
October
25,
2016
ABSTRACT: A framework for the optimal
sparse-control of the probability density function of a jump-diffusion process
is presented. This framework is based on the partial integro-differential
Fokker-Planck (FP) equation that governs the time evolution of the probability
density function of this process. In the stochastic process and, correspondingly,
in the FP model the control function enters as a time-dependent coefficient.
The objectives of the control are to minimize a discrete-in-time, resp.
continuous-in-time, tracking functionals and its L2- and L1-costs, where the
latter is considered to promote control sparsity. An efficient proximal scheme
for solving these optimal control problems is considered. Results of numerical
experiments are presented to validate the theoretical results and the
computational effectiveness of the proposed control framework.