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We develop and analyze a method for stochastic simulation optimization based on Gaussian process models within a trust-region framework. We focus on settings where the variance of the objective function is large, making accurate estimation…

Optimization and Control · Mathematics 2026-03-10 Mickael Binois , Jeffrey Larson

In this contribution, we are concerned with parameter optimization problems that are constrained by multiscale PDE state equations. As an efficient numerical solution approach for such problems, we introduce and analyze a new relaxed and…

Numerical Analysis · Mathematics 2023-04-13 Tim Keil , Mario Ohlberger

We present a model-based derivative-free method for optimization subject to general convex constraints, which we assume are unrelaxable and accessed only through a projection operator that is cheap to evaluate. We prove global convergence…

Optimization and Control · Mathematics 2022-03-18 Matthew Hough , Lindon Roberts

We propose a model order reduction approach for non-intrusive surrogate modeling of parametric dynamical systems. The reduced model over the whole parameter space is built by combining surrogates in frequency only, built at few selected…

Numerical Analysis · Mathematics 2021-09-23 Fabio Nobile , Davide Pradovera

We propose and analyze a model-based derivative-free (DFO) algorithm for solving bound-constrained optimization problems where the objective function is the composition of a smooth function and a vector of black-box functions. We assume…

Optimization and Control · Mathematics 2024-01-03 Frank E. Curtis , Shima Dezfulian , Andreas Wächter

Scattered data interpolation schemes using kriging and radial basis functions (RBFs) have the advantage of being meshless and dimensional independent, however, for the data sets having insufficient observations, RBFs have the advantage over…

Numerical Analysis · Mathematics 2018-06-12 Pankaj K Mishra , Sankar K Nath , Mrinal K Sen , Gregory E Fasshauer

In this paper, we employ Bayesian optimization to concurrently explore the optimal values for both the shape parameter and the radius in the partition of unity interpolation using radial basis functions. Bayesian optimization is a…

Numerical Analysis · Mathematics 2023-11-09 Roberto Cavoretto , Alessandra De Rossi , Sandro Lancellotti , Federico Romaniello

We investigate a trust-region algorithm to solve a nonconvex optimization problem with $L^p$-regularization for $p\in(0,1)$. The algorithm relies on descent properties of a so-called generalized Cauchy point that can be obtained efficiently…

Optimization and Control · Mathematics 2025-08-22 Harbir Antil , Anna Lentz

We consider unconstrained multi-criteria optimization problems with finite sum objective functions. The proposed algorithm belongs to a non-monotone trust region framework where additional sampling approach is used to govern the sample size…

Optimization and Control · Mathematics 2026-03-13 Nataša Krklec Jerinkić , Luka Rutešić , Ilaria Trombini

We propose a stochastic nonconvex optimization algorithm that achieves almost sure $\tilde{\mathcal{O}}(\epsilon^{-1.5})$ iteration complexity for problems with smooth objective functions and gradients only observable with noise. The…

Optimization and Control · Mathematics 2026-04-30 Yunsoo Ha , Sara Shashaani , Quoc Tran-dinh

We describe the optimization algorithm implemented in the open-source derivative-free solver RBFOpt. The algorithm is based on the radial basis function method of Gutmann and the metric stochastic response surface method of Regis and…

Machine Learning · Computer Science 2021-02-02 Giacomo Nannicini

Interpolation-based methods are well-established and effective approaches for the efficient generation of accurate reduced-order surrogate models. Common challenges for such methods are the automatic selection of good or even optimal…

Numerical Analysis · Mathematics 2024-07-23 Quirin Aumann , Steffen W. R. Werner

In this article, we build on previous work to present an optimization algorithm for nonlinearly constrained multi-objective optimization problems. The algorithm combines a surrogate-assisted derivative-free trust-region approach with the…

Optimization and Control · Mathematics 2023-04-20 Manuel Berkemeier , Sebastian Peitz

We consider Riemannian inequality-constrained optimization problems. Such problems inherit the benefits of Riemannian approach developed in the unconstrained setting and naturally arise from applications in control, machine learning, and…

Optimization and Control · Mathematics 2026-05-12 Mitsuaki Obara , Takayuki Okuno , Akiko Takeda

We develop a trust-region method for minimizing the sum of a smooth term $f$ and a nonsmooth term $h$), both of which can be nonconvex. Each iteration of our method minimizes a possibly nonconvex model of $f + h$ in a trust region. The…

Optimization and Control · Mathematics 2021-08-04 Aleksandr Y. Aravkin , Robert Baraldi , Dominique Orban

We propose a nonsmooth trust-region method for solving optimization problems with locally Lipschitz continuous functions, with application to problems constrained by variational inequalities of the second kind. Under suitable assumptions on…

Optimization and Control · Mathematics 2018-01-17 Constantin Christof , Juan Carlos De Los Reyes , Christian Meyer

We present a stochastic trust-region model-based framework in which its radius is related to the probabilistic models. Especially, we propose a specific algorithm, termed STRME, in which the trust-region radius depends linearly on the…

Optimization and Control · Mathematics 2022-09-30 Xiaoyu Wang , Ya-xiang Yuan

We present a globally convergent method to accelerate density-based topology optimization using projection-based reduced-order models (ROMs) and trust-region methods. To accelerate topology optimization, we replace the large-scale finite…

Numerical Analysis · Mathematics 2021-02-03 Masayuki Yano , Tianci Huang , Matthew J. Zahr

This work introduces a data-driven, non-intrusive reduced-order modeling (ROM) framework that leverages Optimal Transport (OT) for multi-fidelity and parametric problems in two-phase flows modelling. Building upon the success of…

Numerical Analysis · Mathematics 2026-03-30 Moaad Khamlich , Niccolò Tonicello , Federico Pichi , Gianluigi Rozza

The growing availability of computational resources has significantly increased the interest of the scientific community in performing complex multi-physics and multi-domain simulations. However, the generation of appropriate computational…

Numerical Analysis · Mathematics 2026-04-03 Daniele Moretto , Andrea Franceschini , Massimiliano Ferronato