Related papers: On frequency- and time-limited H2-optimal model or…
Implicit regularization refers to the tendency of local search algorithms to converge to low-dimensional solutions, even when such structures are not explicitly enforced. Despite its ubiquity, the mechanism underlying this behavior remains…
In this paper, we investigate optimization problems with nonnegative and orthogonal constraints, where any feasible matrix of size $n \times p$ exhibits a sparsity pattern such that each row accommodates at most one nonzero entry. Our…
In this paper we study an infinite-horizon persistent monitoring problem in a two-dimensional mission space containing a finite number of statically placed targets, at each of which we assume a constant rate of uncertainty accumulation.…
In this work we recast parametrized time dependent optimal control problems governed by partial differential equations in a saddle point formulation and we propose reduced order methods as an effective strategy to solve them. Indeed, on one…
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 lead to poor spurious local solutions. In this paper, we…
Balanced truncation is one of the most common model order reduction schemes. In this paper, we study finite-frequency model order reduction (FF-MOR) problems of linear continuous-time systems within the framework of balanced truncation…
The idea of iterative process optimization based on collected output measurements, or "real-time optimization" (RTO), has gained much prominence in recent decades, with many RTO algorithms being proposed, researched, and developed. While…
We address the stabilization of linear, time-varying parabolic PDEs using finite-dimensional receding horizon controls (RHCs) derived from reduced-order models (ROMs). We first prove exponential stability and suboptimality of the…
Here, we focus on Model Order Reduction (MOR) of non-parametric second-order dynamical systems. In these MOR algorithms, sequences of large and sparse linear systems arise during the model reduction process. Solving such linear systems is…
The classical algorithms for online learning and decision-making have the benefit of achieving the optimal performance guarantees, but suffer from computational complexity limitations when implemented at scale. More recent sophisticated…
We study the distributed optimization problem over a graphon with a continuum of nodes, which is regarded as the limit of the distributed networked optimization as the number of nodes goes to infinity. Each node has a private local cost…
Stably inverting a dynamic system model is the foundation of numerous servo designs. Existing inversion techniques have provided accurate model approximations that are often highly effective in feedforward controls. However, when the…
This article investigates the approximation quality achievable for biobjective minimization problems with respect to the Pareto cone by solutions that are (approximately) optimal with respect to larger ordering cones. When simultaneously…
In this paper we suggest a moment matching method for quadratic-bilinear dynamical systems. Most system-theoretic reduction methods for nonlinear systems rely on multivariate frequency representations. Our approach instead uses univariate…
An adaptive parametric reduced-order modeling method based on interpolating poles of reduced-order models is proposed in this paper. To guarantee correct interpolation, a pole-matching process is conducted to determine which poles of two…
Oscillator Ising machines (OIMs) are networks of coupled oscillators that seek the minimum energy state of an Ising model. Since many NP-hard problems are equivalent to the minimization of an Ising Hamiltonian, OIMs have emerged as a…
We consider Riemannian optimization problems with inequality and equality constraints and analyze a class of Riemannian interior point methods for solving them. The algorithm of interest consists of outer and inner iterations. We show that,…
The higher-order guaranteed lower eigenvalue bounds of the Laplacian in the recent work by Carstensen, Ern, and Puttkammer [Numer. Math. 149, 2021] require a parameter $C_{\mathrm{st},1}$ that is found $\textit{not}$ robust as the…
This paper studies the problem of output agreement in networks of nonlinear dynamical systems under time-varying disturbances. Necessary and sufficient conditions for output agreement are derived for the class of incrementally passive…
Many recent studies on first-order methods (FOMs) focus on \emph{composite non-convex non-smooth} optimization with linear and/or nonlinear function constraints. Upper (or worst-case) complexity bounds have been established for these…