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This paper addresses the $\mathcal{H}_2$-optimal approximation of linear dynamical systems with quadratic-output functions, also known as linear quadratic-output systems. Our major contributions are threefold. First, we derive…

Numerical Analysis · Mathematics 2025-05-07 Sean Reiter , Ion Victor Gosea , Igor Pontes Duff , Serkan Gugercin

Complexity analysis has become an important tool in the convergence analysis of optimization algorithms. For derivative-free optimization algorithms, it is not different. Interestingly, several constants that appear when developing…

Optimization and Control · Mathematics 2024-09-26 A. E. Schwertner , F. N. C. Sobral

We study derivative-free methods for policy optimization over the class of linear policies. We focus on characterizing the convergence rate of these methods when applied to linear-quadratic systems, and study various settings of driving…

Machine Learning · Computer Science 2020-05-19 Dhruv Malik , Ashwin Pananjady , Kush Bhatia , Koulik Khamaru , Peter L. Bartlett , Martin J. Wainwright

Derivative-free - or zeroth-order - optimization (DFO) has gained recent attention for its ability to solve problems in a variety of application areas, including machine learning, particularly involving objectives which are stochastic…

Optimization and Control · Mathematics 2020-08-04 Coralia Cartis , Tyler Ferguson , Lindon Roberts

In this note, we present a derivative-free trust-region (TR) algorithm for reliability based optimization (RBO) problems. The proposed algorithm consists of solving a set of subproblems, in which simple surrogate models of the reliability…

Computation · Statistics 2016-10-04 Tian Gao , Jinglai Li

This paper considers the efficient minimization of the infinite time average of a stationary ergodic process in the space of a handful of design parameters which affect it. Problems of this class, derived from physical or numerical…

Optimization and Control · Mathematics 2019-10-29 Pooriya Beyhaghi , Ryan Alimo , Thomas Bewley

We present a flexible trust region descend algorithm for unconstrained and convexly constrained multiobjective optimization problems. It is targeted at heterogeneous and expensive problems, i.e., problems that have at least one objective…

Optimization and Control · Mathematics 2021-05-27 Manuel Berkemeier , Sebastian Peitz

We study three quadratic models in model-based derivative-free optimization: the minimum norm (MN), minimum Frobenius norm (MFN), and quadratic generalized simplex derivative (QS) models. Despite their widespread use, their approximation…

Optimization and Control · Mathematics 2026-05-14 Yiwen Chen , Warren Hare , Lindon Roberts

The trust region method is an algorithm traditionally used in the field of derivative free optimization. The method works by iteratively constructing surrogate models (often linear or quadratic functions) to approximate the true objective…

Optimization and Control · Mathematics 2017-06-12 Ky Vu , Pierre-Louis Poirion , Claudia D'Ambrosio , Leo Liberti

In this paper (part 1), we describe a derivative-free trust-region method for solving unconstrained optimization problems. We will discuss a method when we relax the model order assumption and use artificial neural network techniques to…

Optimization and Control · Mathematics 2020-05-26 Mostafa Rezapour , Thomas Asaki

We consider an optimization problem related to semi-active damping of vibrating systems. The main problem is to determine the best damping matrix able to minimize influence of the input on the output of the system. We use a minimization…

Dynamical Systems · Mathematics 2017-07-07 Zoran Tomljanović , Christopher Beattie , Serkan Gugercin

In many applications of mathematical optimization, one may wish to optimize an objective function without access to its derivatives. These situations call for derivative-free optimization (DFO) methods. Among the most successful approaches…

Optimization and Control · Mathematics 2025-12-11 Abraar Chaudhry , Katya Scheinberg

We investigate the optimal model reduction problem for large-scale quadratic-bilinear (QB) control systems. Our contributions are threefold. First, we discuss the variational analysis and the Volterra series formulation for QB systems. We…

Numerical Analysis · Mathematics 2017-05-17 Peter Benner , Pawan Goyal , Serkan Gugercin

We consider model-based derivative-free optimization (DFO) for large-scale problems, based on iterative minimization in random subspaces. We provide the first worst-case complexity bound for such methods for convergence to approximate…

Optimization and Control · Mathematics 2024-12-20 Coralia Cartis , Lindon Roberts

In this paper we study the problem of model reduction of linear network systems. We aim at computing a reduced order stable approximation of the network with the same topology and optimal w.r.t. H2 norm error approximation. Our approach is…

Optimization and Control · Mathematics 2019-05-21 I. Necoara , T. C. Ionescu

Derivative-Free optimization (DFO) focuses on designing methods to solve optimization problems without the analytical knowledge of gradients of the objective function. There are two main families of DFO methods: model-based methods and…

Optimization and Control · Mathematics 2015-11-10 W. Hare , M. Jaberipour

This paper presents a finite difference quasi-Newton method for the minimization of noisy functions. The method takes advantage of the scalability and power of BFGS updating, and employs an adaptive procedure for choosing the differencing…

Optimization and Control · Mathematics 2019-01-09 Albert S. Berahas , Richard H. Byrd , Jorge Nocedal

We develop an algorithm that combines model-based and model-free methods for solving a nonlinear optimal control problem with a quadratic cost in which the system model is given by a linear state-space model with a small additive nonlinear…

Optimization and Control · Mathematics 2022-03-23 Yansong Li , Shuo Han

We present a technique for model-based derivative-free optimization called \emph{basis sketching}. Basis sketching consists of taking random sketches of the Vandermonde matrix employed in constructing an interpolation model. This…

Optimization and Control · Mathematics 2023-05-30 Matt Menickelly

Policy optimization has drawn increasing attention in reinforcement learning, particularly in the context of derivative-free methods for linear quadratic regulator (LQR) problems with unknown dynamics. This paper focuses on characterizing…

Optimization and Control · Mathematics 2025-06-17 Weijian Li , Panagiotis Kounatidis , Zhong-Ping Jiang , Andreas A. Malikopoulos