On the Complexity of an Inexact Restoration Method for Constrained Optimization

Bueno, Luis; Martínez, José Mário

doi:10.1137/18m1216146

Cited by 11 publications

(10 citation statements)

References 40 publications

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“…2 ) is better than the bounds of O(ǫ −2 ) proved for the first-order schemes proposed by [9] and by [11], if α > 9. This is not surprising, since our result is obtained using a second-order method to solve the subproblems.…”

Section: Discussionmentioning

confidence: 77%

On the Complexity of an Augmented Lagrangian Method for Nonconvex Optimization

Grapiglia,

Yuan

2019

Preprint

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In this paper we study the worst-case complexity of an inexact Augmented Lagrangian method for nonconvex constrained problems. Assuming that the penalty parameters are bounded, we prove a complexity bound of O(| log(ǫ)|) iterations for the referred algorithm generate an ǫ-approximate KKT point, for ǫ ∈ (0, 1). When the penalty parameters are unbounded, we prove an iteration complexity bound of O ǫ −2/(α−1) , where α > 1 controls the rate of increase of the penalty parameters. For linearly constrained problems, these bounds yield to evaluation complexity, respectively, when suitable p-order methods (p ≥ 2) are used to approximately solve the unconstrained subproblems at each iteration of our Augmented Lagrangian scheme.

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Section: Discussionmentioning

confidence: 77%

On the Complexity of an Augmented Lagrangian Method for Nonconvex Optimization

Grapiglia,

Yuan

2019

Preprint

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“…In this paper we extend the results of [12] and [24]. In [12] the problem (2) is considered without the presence of the constraints h(x, y) = 0.…”

Section: Introductionmentioning

confidence: 70%

“…In [12] the problem (2) is considered without the presence of the constraints h(x, y) = 0. In [24] an Inexact Restoration method with worst-case complexity results is introduced for solving the classical constrained optimization problem. The techniques of [12] and [24] are merged in the present paper in order to handle the constrained optimization problem with inexactness both in the objective function and the constraints.…”

Section: Introductionmentioning

confidence: 99%

“…The so far generated trial point is accepted or not as new iterate according to the decrease of a merit function or using filter criteria [32,36,25,26,46]. Theoretical papers concerning Inexact Restoration methods for constrained optimization include [41,10,24]. Algorithmic variations are discused in [41,27,4,22,25,26,28], and applications may be found in [43,1,23,38,15,37,5,31,30,6,29,14,47].…”

Section: Introductionmentioning

confidence: 99%

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Inexact Restoration for Minimization with Inexact Evaluation both of the Objective Function and the Constraints

Bueno¹,

Larreal²,

Martínez³

2022

Preprint

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In a recent paper an Inexact Restoration method for solving continuous constrained optimization problems was analyzed from the point of view of worst-case functional complexity and convergence. On the other hand, the Inexact Restoration methodology was employed, in a different research, to handle minimization problems with inexact evaluation and simple constraints. These two methodologies are combined in the present report, for constrained minimization problems in which both the objective function and the constraints, as well as their derivatives, are subject to evaluation errors. Together with a complete description of the method, complexity and convergence results will be proved.

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“…The reliability of Inexact Restoration for arbitrary nonlinear optimization problems was assessed in [8]. In [20], the worst-case functional complexity of Inexact Restoration was analyzed. An application to finite-sum minimization was described in [7].…”

Section: Introductionmentioning

confidence: 99%

Economic inexact restoration for derivative-free expensive function minimization and applications

Birgin¹,

Krejić²,

Martínez³

2020

Preprint

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The Inexact Restoration approach has proved to be an adequate tool for handling the problem of minimizing an expensive function within an arbitrary feasible set by using different degrees of precision in the objective function. The Inexact Restoration framework allows one to obtain suitable convergence and complexity results for an approach that rationally combines low-and high-precision evaluations. In the present research, it is recognized that many problems with expensive objective functions are nonsmooth and, sometimes, even discontinuous. Having this in mind, the Inexact Restoration approach is extended to the nonsmooth or discontinuous case. Although optimization phases that rely on smoothness cannot be used in this case, basic convergence and complexity results are recovered. A derivative-free optimization phase is defined and the subproblems that arise at this phase are solved using a regularization approach that take advantage of different notions of stationarity. The new methodology is applied to the problem of reproducing a controlled experiment that mimics the failure of a dam.

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On the Complexity of an Inexact Restoration Method for Constrained Optimization

Cited by 11 publications

References 40 publications

On the Complexity of an Augmented Lagrangian Method for Nonconvex Optimization

On the Complexity of an Augmented Lagrangian Method for Nonconvex Optimization

Inexact Restoration for Minimization with Inexact Evaluation both of the Objective Function and the Constraints

Economic inexact restoration for derivative-free expensive function minimization and applications

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