Convergence of trust region augmented Lagrangian methods using variable fidelity approximation data

Jose, F Rodriguez; John, E Renaud; Layne, T Watson

doi:10.1007/bf01203525

Cited by 109 publications

(64 citation statements)

References 33 publications

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“…One of the most common methods to enforce a constraint is to add a penalization term inside the cost function whose magnitude is adjusted dynamically until the constraint is satisfied. In this respect, a very popular method is the augmented-Lagrangian method [74]. Another more empirical technique consists instead in recovering the constraint a posteriori, i.e.…”

Section: Parameters Constraintsmentioning

confidence: 99%

Numerical Simulation of Sailing Boats: Dynamics, FSI, and Shape Optimization

Lombardi

Parolini

Quarteroni

et al. 2012

Springer Optimization and Its Applications

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The numerical simulation of free-surface flows around sailing boats is a complex topic that addresses multiple mathematical tasks: the correct study of the flow field around a rigid hull, the numerical simulation of the hull dynamics, the deformation of the sails and appendages under transient external conditions like gusts of wind or wave patterns and, overall, the coupling among all these components. In this paper, we present some recent advances that have been achieved in different research topics related to yacht design and performance prediction. In particular, we describe the numerical algorithms that have been developed in the framework of open-source libraries for the simulation of free-surface hydrodynamics and boat dynamics, as well as for the analysis of the fluid-structure interaction between wind and sails. Moreover, an algorithm for shape optimization, based on the solution of the adjoint problem and combined with the Free Form Deformation (FFD) method for the shape parametrization and mesh motion, is presented and discussed. Theoretical and methodological aspects are described and the first preliminary results are reported.

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Section: Parameters Constraintsmentioning

confidence: 99%

Numerical Simulation of Sailing Boats: Dynamics, FSI, and Shape Optimization

Lombardi

Parolini

Quarteroni

et al. 2012

Springer Optimization and Its Applications

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“…Initial approaches to nonlinearly-constrained SBO optimized an approximate merit function which incorporated the nonlinear constraints [70,4]:…”

Section: Surrogate-based Local Minimizationmentioning

confidence: 99%

DAKOTA : a multilevel parallel object-oriented framework for design optimization, parameter estimation, uncertainty quantification, and sensitivity analysis.

Eldred

Vigil

Dalbey

et al. 2011

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The DAKOTA (Design Analysis Kit for Optimization and Terascale Applications) toolkit provides a flexible and extensible interface between simulation codes and iterative analysis methods. DAKOTA contains algorithms for optimization with gradient and nongradient-based methods; uncertainty quantification with sampling, reliability, and stochastic expansion methods; parameter estimation with nonlinear least squares methods; and sensitivity/variance analysis with design of experiments and parameter study methods. These capabilities may be used on their own or as components within advanced strategies such as surrogate-based optimization, mixed integer nonlinear programming, or optimization under uncertainty. By employing object-oriented design to implement abstractions of the key components required for iterative systems analyses, the DAKOTA toolkit provides a flexible and extensible problem-solving environment for design and performance analysis of computational models on high performance computers.This report serves as a theoretical manual for selected algorithms implemented within the DAKOTA software. It is not intended as a comprehensive theoretical treatment, since a number of existing texts cover general optimization theory, statistical analysis, and other introductory topics. Rather, this manual is intended to summarize a set of DAKOTA-related research publications in the areas of surrogate-based optimization, uncertainty quantification, and optimization under uncertainty that provide the foundation for many of DAKOTA's iterative analysis capabilities.4

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“…Step 7 Convergence Test: The convergence of the entire framework is governed by satisfying the KarushKuhn-Tucker conditions as is done by Rodríguez et al 30 and Conn et al . 31 For the implementation used in this research the convergence was determined by the following two inequalities:…”

Section: Variable Fidelity Optimizationmentioning

confidence: 99%

“…Furthermore, for each scaling the first order and quasi-second order methods using BFGS and SR1 were compared. All of the trials were started at the point x = [40,30] T with an initial trust region size of ∆ 0 = 10. The results are summarized in Table 2.…”

Section: A Analytic Two Dimensional Problemmentioning

confidence: 99%

Reliability-based design using variable-fidelity optimization

Gano

Renaud

Agarwal

et al. 2006

Structure and Infrastructure Engineering

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Competitive marketplaces have driven the need for simulation based design optimization to produce efficient and cost effective designs. However, such design practices are typically deterministic and don't take into account model uncertainties or manufacturing tolerances. Deterministic designs may lie on failure driven constraints, resulting in designs characterized by a high probability of failure. Reliability based design optimization (RBDO) methods have been developed to obtain designs that optimize a merit function while ensuring a target reliability level. Unfortunately, these methods are notorious for the high computational expense they require to converge. There has been a considerable effort to reduce the computational cost, many of these methods have used approximations which are not guaranteed to converge to the optimal solution of the original high fidelity problem. In this research variable fidelity methods are used to reduce the cost of RBDO. Variable fidelity methods use a set of models with varying degrees of fidelity and computational expense to reduce the cost of optimization. The variable fidelity RBDO methodology developed in this investigation is demonstrated on two test cases: a nonlinear analytic problem and a high-lift airfoil design problem. For each of these problems the proposed method shows considerable savings for performing RBDO as compared with standard approaches.

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Convergence of trust region augmented Lagrangian methods using variable fidelity approximation data

Cited by 109 publications

References 33 publications

Numerical Simulation of Sailing Boats: Dynamics, FSI, and Shape Optimization

Numerical Simulation of Sailing Boats: Dynamics, FSI, and Shape Optimization

DAKOTA : a multilevel parallel object-oriented framework for design optimization, parameter estimation, uncertainty quantification, and sensitivity analysis.

Reliability-based design using variable-fidelity optimization

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