Numerical Optimisation of Time-Varying Strongly Convex Functions Subject to Time-Varying Constraints
Daniel D Selvaratnam, Iman Shames, Jonathan H Manton, Mohammad Zamani
2018 IEEE Conference on Decision and Control (CDC) | IEEE | Published : 2018
This paper analyses the performance of projected gradient descent on optimisation problems with cost functions and constraints that vary in discrete time. Specifically, strongly convex cost functions with Lipschitz gradient, and a sequence of convex constraints are assumed. Error bounds and suboptimality bounds are derived for a variety of cases, which show convergence to a steady-state. Conditions on the constraint sequence are also presented for guaranteeing finite-time feasibility, and for bounding the distance between successive minimisers. Numerical examples are then presented to validate the analytical results.
Awarded by DST Group
This research is supported by DST Group under Collaborative Research Agreements MYIP #6874, MYIP #5923, and by the Defence Science Institute as an initiative of the State Government of Victoria.