Time-varying convex optimization: Time-structured algorithms and applications
Optimization underpins many of the challenges that science and technology face on a daily
basis. Recent years have witnessed a major shift from traditional optimization paradigms …
basis. Recent years have witnessed a major shift from traditional optimization paradigms …
A nonsmooth dynamical systems perspective on accelerated extensions of ADMM
Recently, there has been great interest in connections between continuous-time dynamical
systems and optimization methods, notably in the context of accelerated methods for smooth …
systems and optimization methods, notably in the context of accelerated methods for smooth …
Escaping spurious local minimum trajectories in online time-varying nonconvex optimization
This paper is concerned with solving online nonconvex optimization problems using simple
gradient-based algorithms with an arbitrary initialization. The main objective is to understand …
gradient-based algorithms with an arbitrary initialization. The main objective is to understand …
On-line non-convex constrained optimization
O Massicot, J Marecek - arXiv preprint arXiv:1909.07492, 2019 - arxiv.org
Time-varying non-convex continuous-valued non-linear constrained optimization is a
fundamental problem. We study conditions wherein a momentum-like regularising term …
fundamental problem. We study conditions wherein a momentum-like regularising term …
The Landscape of Deterministic and Stochastic Optimal Control Problems: One-Shot Optimization Versus Dynamic Programming
Optimal control problems can be solved via a one-shot (single) optimization or a sequence
of optimization using dynamic programming (DP). However, the computation of their global …
of optimization using dynamic programming (DP). However, the computation of their global …
Absence of spurious local trajectories in time-varying optimization: A control-theoretic perspective
In this paper, we study the landscape of an optimization problem whose input data vary over
time. This time-varying problem consists of infinitely-many individual optimization problems …
time. This time-varying problem consists of infinitely-many individual optimization problems …
Time-variation in online nonconvex optimization enables escaping from spurious local minima
A major limitation of online algorithms that track the optimizers of time-varying nonconvex
optimization problems is that they focus on a specific local minimum trajectory, which may …
optimization problems is that they focus on a specific local minimum trajectory, which may …
Pursuit of low-rank models of time-varying matrices robust to sparse and measurement noise
A Akhriev, J Marecek, A Simonetto - … of the AAAI Conference on Artificial …, 2020 - ojs.aaai.org
In tracking of time-varying low-rank models of time-varying matrices, we present a method
robust to both uniformly-distributed measurement noise and arbitrarily-distributed “sparse” …
robust to both uniformly-distributed measurement noise and arbitrarily-distributed “sparse” …
Smoothing property of load variation promotes finding global solutions of time-varying optimal power flow
J Mulvaney-Kemp, S Fattahi… - IEEE Transactions on …, 2021 - ieeexplore.ieee.org
This article analyzes solution trajectories for optimal power flow (OPF) with time-varying
load. Despite its nonlinearity, time-varying OPF is commonly solved every 5–15 min using …
load. Despite its nonlinearity, time-varying OPF is commonly solved every 5–15 min using …
Diminishing regret for online nonconvex optimization
A single nonconvex optimization is NP-hard in the worst case, and so is a sequence of
nonconvex problems viewed separately. For online nonconvex optimization (ONO) …
nonconvex problems viewed separately. For online nonconvex optimization (ONO) …