Related papers: H$_2$ Optimal Model Order Reduction over a Finite …
In the context of Markov decision processes running in continuous time, one of the most intriguing challenges is the efficient approximation of finite horizon reachability objectives. A multitude of sophisticated model checking algorithms…
Chemical reactions modeled by ordinary differential equations are finite-dimensional dissipative dynamical systems with multiple time-scales. They are numerically hard to tackle -- especially when they enter an optimal control problem as…
This paper examines the problem of real-time optimization of networked systems and develops online algorithms that steer the system towards the optimal trajectory without explicit knowledge of the system model. The problem is modeled as a…
A framework is introduced for solving a sequence of slowly changing optimization problems, including those arising in regression and classification applications, using optimization algorithms such as stochastic gradient descent (SGD). The…
In this paper, we consider the problem of controlling a dynamical system such that its trajectories satisfy a temporal logic property in a given amount of time. We focus on multi-affine systems and specifications given as syntactically…
Two-time-scale optimization is a framework introduced in Zeng et al. (2024) that abstracts a range of policy evaluation and policy optimization problems in reinforcement learning (RL). Akin to bi-level optimization under a particular type…
There is a recent surge of interest in nonconvex reformulations via low-rank factorization for stochastic convex semidefinite optimization problem in the purpose of efficiency and scalability. Compared with the original convex formulations,…
A classical reduced order model for dynamical problems involves spatial reduction of the problem size. However, temporal reduction accompanied by the spatial reduction can further reduce the problem size without losing accuracy much, which…
This work studies the linear approximation of high-dimensional dynamical systems using low-rank dynamic mode decomposition (DMD). Searching this approximation in a data-driven approach is formalised as attempting to solve a low-rank…
In this paper, we study optimization problems where the cost function contains time-varying parameters that are unmeasurable and evolve according to linear, yet unknown, dynamics. We propose a solution that leverages control theoretic tools…
In this article a topology optimization method is developed, which is aware of material uncertainties. The uncertainties are handled in a worst-case sense, i.e. the worst possible material distribution over a given uncertainty set is taken…
Interpolatory necessary optimality conditions for $\mathcal{H}_2$-optimal reduced-order modeling of unstructured linear time-invariant (LTI) systems are well-known. Based on previous work on $\mathcal{L}_2$-optimal reduced-order modeling of…
We propose an unconstrained optimization method based on the well-known primal-dual hybrid gradient (PDHG) algorithm. We first formulate the optimality condition of the unconstrained optimization problem as a saddle point problem. We then…
Evaluating solutions to optimization problems is arguably the most important step for heuristic algorithms, as it is used to guide the algorithms towards the optimal solution in the solution search space. Research has shown evaluation…
This paper proposes novel gradient-flow schemes that yield convergence to the optimal point of a convex optimization problem within a \textit{fixed} time from any given initial condition for unconstrained optimization, constrained…
In this paper we study convex bi-level optimization problems for which the inner level consists of minimization of the sum of smooth and nonsmooth functions. The outer level aims at minimizing a smooth and strongly convex function over the…
In this work, we consider methods for solving large-scale optimization problems with a possibly nonsmooth objective function. The key idea is to first specify a class of optimization algorithms using a generic iterative scheme involving…
The aim in model order reduction is to approximate an input-output map described by a large-scale dynamical system with a low-dimensional and cheaper-to-evaluate reduced order model. While high fidelity can be achieved by a variety of…
In this paper, we study the assortment optimization problem under the mixed-logit customer choice model. While assortment optimization has been a major topic in revenue management for decades, the mixed-logit model is considered one of the…
We propose a novel second-order ODE as the continuous-time limit of a Riemannian accelerated gradient-based method on a manifold with curvature bounded from below. This ODE can be seen as a generalization of the ODE derived for Euclidean…