A derivative-free trust-funnel method for equality-constrained nonlinear optimization

Sampaio, Ph. R.; Toint, Philippe L.

doi:10.1007/s10589-014-9715-3

Cited by 24 publications

(12 citation statements)

References 29 publications

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“…Primarily concerned with equality constraints, Sampaio and Toint (2015, 2016) propose a derivative-free variant of trust-funnel methods, a class of methods proposed by Gould and Toint (2010) that avoid the use of both merit functions and filters.…”

Section: Methods For Constrained Optimizationmentioning

confidence: 99%

Derivative-free optimization methods

2019

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Dedicated to the memory of Andrew R. Conn for his inspiring enthusiasm and his many contributions to the renaissance of derivative-free optimization methods. AbstractIn many optimization problems arising from scientific, engineering and artificial intelligence applications, objective and constraint functions are available only as the output of a black-box or simulation oracle that does not provide derivative information. Such settings necessitate the use of methods for derivative-free, or zeroth-order, optimization. We provide a review and perspectives on developments in these methods, with an emphasis on highlighting recent developments and on unifying treatment of such problems in the non-linear optimization and machine learning literature. We categorize methods based on assumed properties of the black-box functions, as well as features of the methods. We first overview the primary setting of deterministic methods applied to unconstrained, non-convex optimization problems where the objective function is defined by a deterministic black-box oracle. We then discuss developments in randomized methods, methods that assume some additional structure about the objective (including convexity, separability and general non-smooth compositions), methods for problems where the output of the black-box oracle is stochastic, and methods for handling different types of constraints.

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Section: Methods For Constrained Optimizationmentioning

confidence: 99%

Derivative-free optimization methods

2019

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“…Following ideas expressed in [51], Conn et al [19] proposed their model-based method, and the first convergence theorem for methods of this type was established by Conn et al [15]. Furthermore, some research [15,17] established the global convergence for model-based trust-region methods under certain assumptions and many variants of model-based derivative-free methods are proposed for various optimization problems [26,56,59]. Efficient implementations and commercial codes are also proposed, such as the oldest DFO package developed by Conn and coworkers [15,19], the UOBYOA and NEWUOA packages presented by Powell [52,53] and the packages UDFO and PSDFO of Colson and Toint [10,11].…”

Section: The Nelder-mead Algorithm Initializationmentioning

confidence: 99%

“…Some model-based methods for constrained derivative-free optimization are also proposed. In [56], a new derivative-free funnel method for equality-constrained nonlinear optimization is presented. This method is of the trust-funnel variety and is based on the use of polynomial interpolation models.…”

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confidence: 99%

Survey of derivative-free optimization

Xi¹,

Sun²,

Chen³

2020

Numerical Algebra, Control &Amp; Optimization

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In this survey paper we present an overview of derivative-free optimization, including basic concepts, theories, derivative-free methods and some applications. To date, there are mainly three classes of derivative-free methods and we concentrate on two of them, they are direct search methods and model-based methods. In this paper, we first focus on unconstrained optimization problems and review some classical direct search methods and model-based methods in turn for these problems. Then, we survey a number of derivativefree approaches for problems with constraints, including an algorithm we proposed for spherical optimization recently.

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“…Here, |•| means the cardinality of a set. We can apply a finite number of substitutions of the points in Z, in fact, at most |Z|−1 points, such that the new resultant set is Λ-poised in B(∆) for a polynomial space P, with dimension |Z| and P 1 n−1 ⊆ P ⊆ P 2 n−1 [51,56,57]. Since the selection of interpolation points and their poisedness are beyond the main scope of this paper, we refer the reader to [21,22,24].…”

Section: Definition 31 ([24]mentioning

confidence: 99%

A Derivative-Free Geometric Algorithm for Optimization on a Sphere

Chen¹

2020

CSIAM-AM

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Optimization on a unit sphere finds crucial applications in science and engineering. However, derivatives of the objective function may be difficult to compute or corrupted by noises, or even not available in many applications. Hence, we propose a Derivative-Free Geometric Algorithm (DFGA) which, to the best of our knowledge, is the first derivative-free algorithm that takes trust region framework and explores the spherical geometry to solve the optimization problem with a spherical constraint. Nice geometry of the spherical surface allows us to pursue the optimization at each iteration in a local tangent space of the sphere. Particularly, by applying Householder and Cayley transformations, DFGA builds a quadratic trust region model on the local tangent space such that the local optimization can essentially be treated as an unconstrained optimization. Under mild assumptions, we show that there exists a subsequence of the iterates generated by DFGA converging to a stationary point of this spherical optimization. Furthermore, under the Łojasiewicz property, we show that all the iterates generated by DFGA will converge with at least a linear or sublinear convergence rate. Our numerical experiments on solving the spherical location problems, subspace clustering and image segmentation problems resulted from hypergraph partitioning, indicate DFGA is very robust and efficient for solving optimization on a sphere without using derivatives.

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A derivative-free trust-funnel method for equality-constrained nonlinear optimization

Cited by 24 publications

References 29 publications

Derivative-free optimization methods

Derivative-free optimization methods

Survey of derivative-free optimization

A Derivative-Free Geometric Algorithm for Optimization on a Sphere

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