New Sequential and Parallel Derivative-Free Algorithms for Unconstrained Minimization

García-Palomares, Ubaldo M.; Rodrı́guez, José F.

doi:10.1137/s1052623400370606

Cited by 57 publications

(65 citation statements)

References 28 publications

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“…Instead, the models are constructed via least-squares fits [121] or interpolation techniques [72,74,220]. As if this were not confusing enough, the term "derivative-free" appears in the titles of other papers [115,173,174,175] in reference to algorithms that do not explicitly construct a local model of the functions involved.…”

Section: 4mentioning

confidence: 99%

Optimization by Direct Search: New Perspectives on Some Classical and Modern Methods

2003

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Abstract. Direct search methods are best known as unconstrained optimization techniques that do not explicitly use derivatives. Direct search methods were formally proposed and widely applied in the 1960s but fell out of favor with the mathematical optimization community by the early 1970s because they lacked coherent mathematical analysis. Nonetheless, users remained loyal to these methods, most of which were easy to program, some of which were reliable. In the past fifteen years, these methods have seen a revival due, in part, to the appearance of mathematical analysis, as well as to interest in parallel and distributed computing. This review begins by briefly summarizing the history of direct search methods and considering the special properties of problems for which they are well suited. Our focus then turns to a broad class of methods for which we provide a unifying framework that lends itself to a variety of convergence results. The underlying principles allow generalization to handle bound constraints and linear constraints. We also discuss extensions to problems with nonlinear constraints.

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Section: 4mentioning

confidence: 99%

Optimization by Direct Search: New Perspectives on Some Classical and Modern Methods

2003

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“…When all the coordinate directions have been explored (inner for loop, i.e. steps [3][4][5][6][7][8][9][10][11][12], the algorithm computes (by steps [13][14][15][16][17][18] the new values ξ k+1 , ǫ k+1 , and η k+1 for the sufficient reduction, penalty and feasibility violation parameters, respectively. In particular, provided that no discrete variable has been updated and that the tentative steps along discrete coordinates are equal to one, the sufficient reduction parameter is decreased.…”

Section: End Formentioning

confidence: 99%

“…In [20] a linesearch strategy for linearly constrained problems [22] is adopted for the solution of Problem (1). In [9] the derivative free algorithms proposed in [10] are extended to the solution of mixed variable problems with bound constraints only. In [24] a probabilistic method using surrogate models for the optimization of computationally expensive mixed-integer black-box problems is proposed.…”

Section: Introductionmentioning

confidence: 99%

Derivative-Free Methods for Mixed-Integer Constrained Optimization Problems

Liuzzi

Lucidi

Rinaldi

2014

J Optim Theory Appl

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Methods which do not use any derivative information are becoming popular among researchers, since they allow to solve many real-world engineering problems. Such problems are frequently characterized by the presence of discrete variables which can further complicate the optimization process. In this paper, we propose derivative-free algorithms for solving Mixed Integer NonLinear Programming (MINLP) problems with general nonlinear constraints and explicit handling of bound constraints on the problem variables. We use an exterior penalty approach to handle the general nonlinear constraints and a local search approach to take into account the presence of discrete variables. We show that the proposed algorithms globally converge to points satisfying different necessary optimality conditions. We report a computational experience and a comparison with a well-known derivative-free optimization software package, i.e. NOMAD, on a set of test problems. Furthermore, we employ the proposed methods and NOMAD to solve a real problem concerning the optimal design of an industrial electric motor. This allows to show that the method converging to the better extended stationary points obtains the best solution also from an applicative point of view.

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“…(1) has been frequently used by monotone algorithms: given xi, di E En, the algorithm must determine a stepsize Xi so that the new iterate xi+l gives a sufficient decrease in the function value, Under suitable assumptions (Al-A4 below) a (sub)sequence fulfilling (1) converges to a point Z satisfying the first order necessary optimality condition; namely V f ( 5 ) = O [14]. Additional conditions, mainly in the choice of {di)y, are obviously required to ensure a superlinear rate of convergence.…”

Section: Introductionmentioning

confidence: 99%

“…This paper adapts a sufficient decrease condition that does not require the computation of derivatives [5,151. Therefore, it can be used in derivative-free optimization and gradient-related algorithms.…”

Section: Introductionmentioning

confidence: 99%

Non Monotone Algorithms for Unconstrained Minimization: Upper Bounds on Function Values

García-Palomares

IFIP International Federation for Information Processing

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New Sequential and Parallel Derivative-Free Algorithms for Unconstrained Minimization

Cited by 57 publications

References 28 publications

Optimization by Direct Search: New Perspectives on Some Classical and Modern Methods

Optimization by Direct Search: New Perspectives on Some Classical and Modern Methods

Derivative-Free Methods for Mixed-Integer Constrained Optimization Problems

Non Monotone Algorithms for Unconstrained Minimization: Upper Bounds on Function Values

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