Derivative-Free Optimization

Krämer, Oliver; Ciaurri, David Echeverría; Koziel, Slawomir

doi:10.1007/978-3-642-20859-1_4

Cited by 71 publications

(39 citation statements)

References 54 publications

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“…This sampling step can be replaced by an optimization method such as Trust Region [36][37][38] or Line Search [39,40]. However, in order for it to work, some regularities must be satisfied by the gradient approximation (18b) [41][42][43][44][45], for instance, smoothness, which in practice is not necessarily the case.…”

Section: Sampling Method-approaching the Posteriormentioning

confidence: 99%

A Robust Non-Gaussian Data Assimilation Method for Highly Non-Linear Models

2018

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Abstract:In this paper, we propose an efficient EnKF implementation for non-Gaussian data assimilation based on Gaussian Mixture Models and Markov-Chain-Monte-Carlo (MCMC) methods. The proposed method works as follows: based on an ensemble of model realizations, prior errors are estimated via a Gaussian Mixture density whose parameters are approximated by means of an Expectation Maximization method. Then, by using an iterative method, observation operators are linearized about current solutions and posterior modes are estimated via a MCMC implementation. The acceptance/rejection criterion is similar to that of the Metropolis-Hastings rule. Experimental tests are performed on the Lorenz 96 model. The results show that the proposed method can decrease prior errors by several order of magnitudes in a root-mean-square-error sense for nearly sparse or dense observational networks.

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Section: Sampling Method-approaching the Posteriormentioning

confidence: 99%

A Robust Non-Gaussian Data Assimilation Method for Highly Non-Linear Models

2018

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“…Often, work involves evaluating different solvers for smooth or noisy constraint functions [7] or interpolation and approximation [6]. This paper takes the latter approach, by sampling the function for the constraint instead of knowing it outright.…”

Section: Derivative Free Optimizationmentioning

confidence: 99%

User-centric exergaming with fine-grain activity recognition

Mortazavi¹,

Lee²,

Sarrafzadeh³

2014

Proceedings of the 2014 ACM International Joint Conference on Pervasive and Ubiquitous Computing: Adjunct Publication

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Exergaming, the use of activity, exercise, and information in video games, has been a growing field for the promotion of wellness and for preventing and treating obesity. Realistic exergaming requires movements that are adapted from detailed, fine-grain motions. An appropriate, active exergame requires a user-centric design, allowing for accurate motion recognition as well as a real-time responsiveness, often balancing accuracy with latency. This paper presents a framework for such an exergaming system, specializing on human interaction. This system includes a method for dynamically altering the algorithm to analyze the trade-off between classification accuracy and real-time responsiveness, allowing for a unique, tailored, interactive experience.

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“…Before we derive the numerical optimization algorithm, we first present the following definition of simplex gradient [34]. …”

Section: Derivative-free Optimizationmentioning

confidence: 99%

“…Gradient, or its estimation, based extremum seeking control is the most straightforward approach [32,33], but the requirement for continuous measurement and approximation of the gradient or the Hessian is very strong. On the other hand, rather than approximating the gradient or the Hessian, derivative-free numerical optimization methods rely on building an approximate model of the objective function based on the sample function values [34].…”

Section: Introductionmentioning

confidence: 99%

Gradient-free numerical optimization-based extremum seeking control for multiagent systems

Vweza

Chong

Lee

2015

Int. J. Control Autom. Syst.

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In this article, we develop a model-and gradient-free numerical optimization-based extremum seeking control scheme to solve the problem of formation control and target tracking in multiagent systems. Unlike in conventional gradient-based extremum seeking control, we do not make the strong assumption that the gradient and/or the Hessian of the objective function can be analytically computed from continuously measured system states. Rather, we employ a derivative-free numerical optimization method that directly builds an approximate model of the objective function. After showing the global convergence of the optimization algorithm, we use a regulator to drive the states of the system to the optimizer of the unknown performance function. We demonstrate the performance of the control scheme by simulations where we control three agents that are given a random initial position and are required to maintain an equilateral triangle formation while tracking and localizing a source signal with unknown spatial dynamics.

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Derivative-Free Optimization

Cited by 71 publications

References 54 publications

A Robust Non-Gaussian Data Assimilation Method for Highly Non-Linear Models

A Robust Non-Gaussian Data Assimilation Method for Highly Non-Linear Models

User-centric exergaming with fine-grain activity recognition

Gradient-free numerical optimization-based extremum seeking control for multiagent systems

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