A derivative-free method for solving box-constrained underdetermined nonlinear systems of equations

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

doi:10.1016/j.amc.2012.09.056

Cited by 13 publications

(19 citation statements)

References 22 publications

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“…For other problems where f * is not known, the absolute difference between the objective function values of consecutive iterations can be compared with ε f to decide termination. Besides, if (12) does not hold, the algorithm has an alternative stopping rule based on the maximum number of iterations (k max ).…”

Section: Stopping Criteriamentioning

confidence: 99%

“…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%

See 1 more Smart Citation

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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Section: Stopping Criteriamentioning

confidence: 99%

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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show abstract

“…We use the BCDF-QNB algorithm [11] in the restoration phase of the DFF algorithm. BCDF-QNB (Box-Constrained Derivative-Free Quasi Newton), based on the Broyden update formula, is a derivative-free method for solving underdetermined nonlinear systems with bound constraints.…”

Section: Restoration Phasementioning

confidence: 99%

“…The restoration phase must solve an underdetermined nonlinear system with bound constraints. In our implementation we performed this phase using the derivative-free method developed in [11].…”

Section: Introductionmentioning

confidence: 99%

An inexact restoration derivative-free filter method for nonlinear programming

Echebest¹,

Schuverdt

Vignau³

2015

Comp. Appl. Math.

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An inexact restoration derivative-free filter method for nonlinear programming is introduced in this paper. Each iteration is composed of a restoration phase, which reduces a measure of infeasibility, and an optimization phase, which reduces the objective function. The restoration phase is solved using a derivative-free method for solving underdetermined nonlinear systems with bound constraints, developed previously by the authors. An alternative for solving the optimization phase is considered. Theoretical convergence results and some preliminary numerical experiments are presented.

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“…Many of them are combinations of Newton methods with some strategies taking into account the constraint set. Strategies based on projections, trust region, active set and gradient methods have been used; see, e.g., [3,5,10,18,19,20,24,25,26,31,32,33]. A Newton conditional gradient (Newton-CondG) method was proposed in [15] (see [16] for its inexact version) to compute approximate solutions of (3).…”

Section: Introductionmentioning

confidence: 99%

On the global convergence of an inexact quasi-Newton conditional gradient method for constrained nonlinear systems

Gonçalves

Oliveira

2019

Numer Algor

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In this paper, we propose a globally convergent method for solving constrained nonlinear systems. The method combines an efficient Newton conditional gradient method with a derivativefree and nonmonotone linesearch strategy. The global convergence analysis of the proposed method is established under suitable conditions, and some preliminary numerical experiments are given to illustrate its performance.

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A derivative-free method for solving box-constrained underdetermined nonlinear systems of equations

Cited by 13 publications

References 22 publications

Combining Filter Method and Dynamically Dimensioned Search for Constrained Global Optimization

Combining Filter Method and Dynamically Dimensioned Search for Constrained Global Optimization

An inexact restoration derivative-free filter method for nonlinear programming

On the global convergence of an inexact quasi-Newton conditional gradient method for constrained nonlinear systems

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