53,419 research outputs found
Guidance, flight mechanics and trajectory optimization. Volume 11 - Guidance equations for orbital operations
Mathematical formulation of guidance equations and solutions for orbital space mission
A Coordinate-Descent Algorithm for Tracking Solutions in Time-Varying Optimal Power Flows
Consider a polynomial optimisation problem, whose instances vary continuously
over time. We propose to use a coordinate-descent algorithm for solving such
time-varying optimisation problems. In particular, we focus on relaxations of
transmission-constrained problems in power systems.
On the example of the alternating-current optimal power flows (ACOPF), we
bound the difference between the current approximate optimal cost generated by
our algorithm and the optimal cost for a relaxation using the most recent data
from above by a function of the properties of the instance and the rate of
change to the instance over time. We also bound the number of floating-point
operations that need to be performed between two updates in order to guarantee
the error is bounded from above by a given constant
Universal Convexification via Risk-Aversion
We develop a framework for convexifying a fairly general class of
optimization problems. Under additional assumptions, we analyze the
suboptimality of the solution to the convexified problem relative to the
original nonconvex problem and prove additive approximation guarantees. We then
develop algorithms based on stochastic gradient methods to solve the resulting
optimization problems and show bounds on convergence rates. %We show a simple
application of this framework to supervised learning, where one can perform
integration explicitly and can use standard (non-stochastic) optimization
algorithms with better convergence guarantees. We then extend this framework to
apply to a general class of discrete-time dynamical systems. In this context,
our convexification approach falls under the well-studied paradigm of
risk-sensitive Markov Decision Processes. We derive the first known model-based
and model-free policy gradient optimization algorithms with guaranteed
convergence to the optimal solution. Finally, we present numerical results
validating our formulation in different applications
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