Coordinate search algorithms in multilevel optimization

Frandi, Emanuele; Papini, Alessandra

doi:10.1080/10556788.2013.841691

Cited by 18 publications

(32 citation statements)

References 16 publications

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“…We show that in both cases we are able to obtain solutions accurate to the level of the discretization error with a computational cost proportional to the number of variables in the problem, thus attaining (at least approximately) an efficiency similar to that of a linear full-multigrid method. This property is not preserved, instead, by the algorithm described in [6].…”

Section: Introductionmentioning

confidence: 88%

“…Moreover, if the above procedure is iterated on the finest level, it can be proved that the resulting algorithm converges globally to a stationary point [6,12].…”

Section: Derivative-free Multilevel Optimizationmentioning

confidence: 98%

“…Several approaches for solving problems of the form (2) have been examined in the literature [7,8,12]. Here, we consider the multilevel v-cycle correction scheme defined in [6], which builds on the framework introduced in [ …”

Section: Derivative-free Multilevel Optimizationmentioning

confidence: 99%

“…Indeed, in [6] we introduced a Coordinate Search multilevel scheme based on updates of Gauss-Seidel type, which, by exploiting a sequence of smaller optimization problems to accelerate the computation of a finest-level solution, is capable to obtain approximate solutions to large-scale problems in a reasonable time.…”

Section: Introductionmentioning

confidence: 99%

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Improving Direct Search algorithms by multilevel optimization techniques

Frandi

Papini

2015

Optimization Methods and Software

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Direct Search algorithms are classical derivative-free methods for optimization. Though endowed with solid theoretical properties, they are not well suited for large-scale problems due to slow convergence and scaling issues. In this paper, we discuss how, on problems for which a hierarchy of objective functions is available, such limitations can be circumvented by using multilevel schemes which are able to accelerate the computation of a finest level solution. Starting from a previously introduced derivative-free multilevel method, based on Coordinate Search optimization with a sampling strategy of Gauss-Seidel type, we consider also the use of sampling strategies of Jacobi type, and present several algorithmic variations. We justify our choices by performing experiments on two model problems, showing that a performance close to multigrid optimality can be observed in practice.

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Section: Introductionmentioning

confidence: 88%

“…Moreover, if the above procedure is iterated on the finest level, it can be proved that the resulting algorithm converges globally to a stationary point [6,12].…”

Section: Derivative-free Multilevel Optimizationmentioning

confidence: 98%

Section: Derivative-free Multilevel Optimizationmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Improving Direct Search algorithms by multilevel optimization techniques

Frandi

Papini

2015

Optimization Methods and Software

Self Cite

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“…This structure will need a nested optimization methodology. Methodologies, such as in multilevel optimization-based algorithms, are well developed [33][34][35][36]. Of course, these methodologies require high computing power; however, such power is almost available nowadays.…”

Section: Model Optimization Proceduresmentioning

confidence: 99%

Mathematical framework for recursive model-based system design

2015

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In this paper, we introduce a mathematical framework that allows the designer to consider more of the proposed ideas and options in conceptual design phase into the design process. The proposed model allows for dynamical relationship between the system's high-level requirements and the detailed design parameters, where an optimization engine can optimize over the design parameters and variables for a given range in the requirement. This is done by proposing an input/output block structure named recursive design modular (RDM). The output of RDM is the functions that the system supposes to perform at particular level. The input of RDM is the design parameters that control the required behaviour through a set of mapping or transformation.Keywords Model-based system design · Systems engineering · Model-based system engineering

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