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In recent decades, cold atom experiments have become increasingly complex. While computers control most parameters, optimization is mostly done manually. This is a time-consuming task for a high-dimensional parameter space with unknown…

Quantum Physics · Physics 2013-09-03 I. Geisel , K. Cordes , J. Mahnke , S. Jöllenbeck , J. Ostermann , J. Arlt , W. Ertmer , C. Klempt

Real-world experiments involve batched & delayed feedback, non-stationarity, multiple objectives & constraints, and (often some) personalization. Tailoring adaptive methods to address these challenges on a per-problem basis is infeasible,…

Machine Learning · Computer Science 2024-11-11 Ethan Che , Daniel R. Jiang , Hongseok Namkoong , Jimmy Wang

Point discretization of curved surfaces is required in many applications ranging from object rendering to the solution of surface partial differential equations (PDEs). These applications often impose that surfaces are sampled with local…

Computational Engineering, Finance, and Science · Computer Science 2026-05-06 Lennart J. Schulze , Ivo F. Sbalzarini

Bayesian approaches developed to solve the optimal design of sequential experiments are mathematically elegant but computationally challenging. Recently, techniques using amortization have been proposed to make these Bayesian approaches…

Machine Learning · Computer Science 2022-06-20 Tom Blau , Edwin V. Bonilla , Iadine Chades , Amir Dezfouli

This paper considers an optimization problem for a dynamical system whose evolution depends on a collection of binary decision variables. We develop scalable approximation algorithms with provable suboptimality bounds to provide…

Optimization and Control · Mathematics 2016-10-31 Insoon Yang , Samuel A. Burden , Ram Rajagopal , S. Shankar Sastry , Claire J. Tomlin

Quantum optimization algorithms hold the promise of solving classically hard, discrete optimization problems in practice. The requirement of encoding such problems in a Hamiltonian realized with a finite -- and currently small -- number of…

Quantum Physics · Physics 2023-07-10 Yifeng Rocky Zhu , David Joseph , Cong Ling , Florian Mintert

We consider adaptive finite element methods for second-order elliptic PDEs, where the arising discrete systems are not solved exactly. For contractive iterative solvers, we formulate an adaptive algorithm which monitors and steers the…

Numerical Analysis · Mathematics 2021-07-14 Gregor Gantner , Alexander Haberl , Dirk Praetorius , Stefan Schimanko

We devise an a posteriori error estimator for an affine optimal control problem subject to a semilinear elliptic PDE and control constraints. To approximate the problem, we consider a semidiscrete scheme based on the variational…

Optimization and Control · Mathematics 2025-05-08 Francisco Fuica , Nicolai Jork

We address the design and synthesis of optimal control strategies for high-dimensional stochastic dynamical systems. Such systems may be deterministic nonlinear systems evolving from random initial states, or systems driven by random…

Numerical Analysis · Mathematics 2020-08-26 Panos Lambrianides , Qi Gong , Daniele Venturi

This paper studies the distributed optimization problem with possibly nonidentical local constraints, where its global objective function is composed of $N$ convex functions. The aim is to solve the considered optimization problem in a…

Optimization and Control · Mathematics 2022-08-26 Hongzhe Liu , Wenwu Yu , Guanghui Wen , Wei Xing Zheng

We propose, analyze, and test new iterative solvers for large-scale systems of linear algebraic equations arising from the finite element discretization of reduced optimality systems defining the finite element approximations to the…

Numerical Analysis · Mathematics 2023-12-20 Ulrich Langer , Richard Löscher , Olaf Steinbach , Huidong Yang

We analyze adaptive mesh-refining algorithms for conforming finite element discretizations of certain non-linear second-order partial differential equations. We allow continuous polynomials of arbitrary, but fixed polynomial order. The…

Numerical Analysis · Mathematics 2014-03-14 Michael Feischl , Thomas Führer , Dirk Praetorius

We develop and analyze a set of new sequential simulation-optimization algorithms for large-scale multi-dimensional discrete optimization via simulation problems with a convexity structure. The "large-scale" notion refers to that the…

Optimization and Control · Mathematics 2022-01-20 Haixiang Zhang , Zeyu Zheng , Javad Lavaei

Neural networks have recently been employed as material discretizations within adjoint optimization frameworks for inverse problems and topology optimization. While advantageous regularization effects and better optima have been found for…

Machine Learning · Computer Science 2024-07-26 Leon Herrmann , Ole Sigmund , Viola Muning Li , Christian Vogl , Stefan Kollmannsberger

A new gradient-based adaptive sampling method is proposed for design of experiments applications which balances space filling, local refinement, and error minimization objectives while reducing reliance on delicate tuning parameters. High…

Methodology · Statistics 2024-05-09 Lucas Caparini , Gwynn J. Elfring , Mauricio Ponga

In this paper we consider a distributed optimization scenario in which a set of agents has to solve a convex optimization problem with separable cost function, local constraint sets and a coupling inequality constraint. We propose a novel…

Systems and Control · Computer Science 2018-04-25 Ivano Notarnicola , Giuseppe Notarstefano

We present a novel energy-based numerical analysis of semilinear diffusion-reaction boundary value problems. Based on a suitable variational setting, the proposed computational scheme can be seen as an energy minimisation approach. More…

Numerical Analysis · Mathematics 2022-02-16 Mario Amrein , Pascal Heid , Thomas P. Wihler

We present a novel framework for PDE-constrained $r$-adaptivity of high-order meshes. The proposed method formulates mesh movement as an optimization problem, with an objective function defined as a convex combination of a mesh quality…

Numerical Analysis · Mathematics 2025-07-03 Tzanio Kolev , Boyan Lazarov , Ketan Mittal , Mathias Schmidt , Vladimir Tomov

Due to the increasing demand for high performance and cost reduction within the framework of complex system design, numerical optimization of computationally costly problems is an increasingly popular topic in most engineering fields. In…

Optimization and Control · Mathematics 2018-06-12 Julien Pelamatti , Loïc Brevault , Mathieu Balesdent , El-Ghazali Talbi , Yannick Guerin

We present a powerful general framework for designing data-dependent optimization algorithms, building upon and unifying recent techniques in adaptive regularization, optimistic gradient predictions, and problem-dependent randomization. We…

Machine Learning · Statistics 2015-10-14 Mehryar Mohri , Scott Yang