Related papers: Second-Order Switching Time Optimization for Switc…
This paper studies the design of feedback controllers to steer a switching linear time-invariant dynamical system towards the solution trajectory of a time-varying convex optimization problem. We propose two types of controllers: (i) a…
Bilevel optimization has been widely applied in many important machine learning applications such as hyperparameter optimization and meta-learning. Recently, several momentum-based algorithms have been proposed to solve bilevel optimization…
We propose a novel second-order optimization framework for training the emerging deep continuous-time models, specifically the Neural Ordinary Differential Equations (Neural ODEs). Since their training already involves expensive gradient…
Recently a majorization method for optimizing partition functions of log-linear models was proposed alongside a novel quadratic variational upper-bound. In the batch setting, it outperformed state-of-the-art first- and second-order…
This paper deals with stabilization of discrete-time switched linear systems when explicit knowledge of the state-space models of their subsystems is not available. Given the set of admissible switches between the subsystems, the admissible…
We consider stochastic optimization with delayed gradients where, at each time step $t$, the algorithm makes an update using a stale stochastic gradient from step $t - d_t$ for some arbitrary delay $d_t$. This setting abstracts asynchronous…
The paper is devoted to deriving novel second-order necessary and sufficient optimality conditions for local minimizers in rather general classes of nonsmooth unconstrained and constrained optimization problems in finite-dimensional spaces.…
We describe an algorithm for the numerical solution of second order linear differential equations in the highly-oscillatory regime. It is founded on the recent observation that the solutions of equations of this type can be accurately…
This paper investigates the optimal co-design of logical and continuous controls for switched linear systems governed by controlled logical switching dynamics. Unlike traditional switched systems with arbitrary or state-dependent switching,…
This paper concerns a first-order algorithmic technique for a class of optimal control problems defined on switched-mode hybrid systems. The salient feature of the algorithm is that it avoids the computation of Fr\'echet or G\^ateaux…
We investigate modifications to Bayesian Optimization for a resource-constrained setting of sequential experimental design where changes to certain design variables of the search space incur a switching cost. This models the scenario where…
Distributed optimization for resource allocation problems is investigated and a sub-optimal continuous-time algorithm is proposed. Our algorithm has lower order dynamics than others to reduce burdens of computation and communication, and is…
We provide several quantum algorithms for continuous optimization that do not require gradient estimation. Instead, we encode the optimization problem into the dynamics of a physical system and coherently simulate the time evolution. We…
In this paper we consider distributed optimization problems in which the cost function is separable, i.e., a sum of possibly non-smooth functions all sharing a common variable, and can be split into a strongly convex term and a convex one.…
Novel nonlinear damping control is proposed for the second-order systems. The proportional output feedback is combined with the damping term which is quadratic to the output derivative and inverse to the set-point distance. The global…
Trajectory optimization considers the problem of deciding how to control a dynamical system to move along a trajectory which minimizes some cost function. Differential Dynamic Programming (DDP) is an optimal control method which utilizes a…
Optimization algorithms have a rich and fundamental relationship with ordinary differential equations given by its continuous-time limit. When the cost function varies with time -- typically in response to a dynamically changing environment…
This paper presents a new fast and robust algorithm that provides fuel-optimal impulsive control input sequences that drive a linear time-variant system to a desired state at a specified time. This algorithm is applicable to a broad class…
In this paper, online convex optimization is applied to the problem of controlling linear dynamical systems. An algorithm similar to online gradient descent, which can handle time-varying and unknown cost functions, is proposed. Then,…
This paper proposes a novel method for designing finite-horizon discrete-valued switching signals in linear switched systems based on discreteness-promoting regularization. The inherent combinatorial optimization problem is reformulated as…