An inexact restoration derivative-free filter method for nonlinear programming

Echebest, Nélida Ester; Schuverdt, María Laura; Vignau, Raúl Pedro

doi:10.1007/s40314-015-0253-0

Cited by 14 publications

(17 citation statements)

References 24 publications

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“…Echebest, Schuverdt and Vignau (2015) develop a derivative-free method in the inexact feasibility restoration filter method framework of Gonzaga, Karas and Vanti (2004). Echebest et al.…”

Section: Methods For Constrained Optimizationmentioning

confidence: 99%

“…Echebest et al. (2015) employ fully linear models of the objective and constraint functions and show that the resulting limit points are first-order KKT points.…”

Section: Methods For Constrained Optimizationmentioning

confidence: 99%

“…Because these models are stochastic, point acceptability is determined by criteria such as probability of filter acceptability or expected area of dominated region (in the filter space). Echebest et al [2015] develop a derivative-free method in the inexact feasibility restoration filter method framework of Gonzaga et al [2004]. Echebest et al [2015] employ fully linear models of the objective and constraint functions and show that the resulting limit points are first-order KKT points.…”

Section: Simulation-based Constraintsmentioning

confidence: 99%

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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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“…Echebest, Schuverdt and Vignau (2015) develop a derivative-free method in the inexact feasibility restoration filter method framework of Gonzaga, Karas and Vanti (2004). Echebest et al.…”

Section: Methods For Constrained Optimizationmentioning

confidence: 99%

“…Echebest et al. (2015) employ fully linear models of the objective and constraint functions and show that the resulting limit points are first-order KKT points.…”

Section: Methods For Constrained Optimizationmentioning

confidence: 99%

Section: Simulation-based Constraintsmentioning

confidence: 99%

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Derivative-free optimization methods

2019

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“…The filter method uses the concept of dominance, borrowed from multi-objective optimization, to build a filter that accepts iterates if they improve the objective function or improve a constraint violation function based on the Pareto dominance rule. Ever since, an abundance of filter-based approaches have been proposed [4,10,11,14,15,21,31,46,48].…”

Section: Introductionmentioning

confidence: 99%

Filter-based stochastic algorithm for global optimization

et al. 2020

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We propose the general Filter-based Stochastic Algorithm (FbSA) for the global optimization of nonconvex and nonsmooth constrained problems. Under certain conditions on the probability distributions that generate the sample points, almost sure convergence is proved. In order to optimize problems with computationally expensive black-box objective functions, we develop the FbSA-RBF algorithm based on the general FbSA and assisted by Radial Basis Function (RBF) surrogate models to approximate the objective function. At each iteration, the resulting algorithm constructs/updates a surrogate model of the objective function and generates trial points using a dynamic coordinate search strategy similar to the one used in the Dynamically Dimensioned Search method. To identify a promising best trial point, a non-dominance concept based on the values of the surrogate model and the constraint violation at the trial points is used. Theoretical results concerning the sufficient conditions for the almost surely convergence of the algorithm are presented. Preliminary numerical experiments show that the FbSA-RBF is competitive when compared with other known methods in the literature.

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“…Filter methods have been combined with trust-region approaches [2,3], SQP techniques [4,5], inexact restoration algorithms [6,7], interior point strategies [8] and line-search algorithms [9,10,11]. They also have been extended to other areas of optimization such as nonlinear equations and inequalities [12,13,14,15], nonsmooth optimization [16,17], unconstrained optimization [18,19], complementarity problems [20,21] and derivativefree optimization [22,23,24,25].…”

Section: Introductionmentioning

confidence: 99%

Combining Filter Method and Dynamically Dimensioned Search for Constrained Global Optimization

Macêdo

Costa

Rocha

et al. 2017

Computational Science and Its Applications – ICCSA 2017

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In this work we present an algorithm that combines the filter technique and the dynamically dimensioned search (DDS) for solving nonlinear and nonconvex constrained global optimization problems. The DDS is a stochastic global algorithm for solving bound constrained problems that in each iteration generates a randomly trial point perturbing some coordinates of the current best point. The filter technique controls the progress related to optimality and feasibility defining a forbidden region of points refused by the algorithm. This region can be given by the flat or slanting filter rule. The proposed algorithm does not compute or approximate any derivatives of the objective and constraint functions. Preliminary experiments show that the proposed algorithm gives competitive results when compared with other methods.

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An inexact restoration derivative-free filter method for nonlinear programming

Cited by 14 publications

References 24 publications

Derivative-free optimization methods

Derivative-free optimization methods

Filter-based stochastic algorithm for global optimization

Combining Filter Method and Dynamically Dimensioned Search for Constrained Global Optimization

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