Journal ArticleDOI
A Trust Region Framework for Managing the Use of Approximation Models in Optimization
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TLDR
An analytically robust, globally convergent approach to managing the use of approximation models of varying fidelity in optimization, based on the trust region idea from nonlinear programming, which is shown to be provably convergent to a solution of the original high-fidelity problem.Abstract:
This paper presents an analytically robust, globally convergent approach to managing the use of approximation models of various fidelity in optimization. By robust global behavior we mean the mathematical assurance that the iterates produced by the optimization algorithm, started at an arbitrary initial iterate, will converge to a stationary point or local optimizer for the original problem. The approach we present is based on the trust region idea from nonlinear programming and is shown to be provably convergent to a solution of the original high-fidelity problem. The proposed method for managing approximations in engineering optimization suggests ways to decide when the fidelity, and thus the cost, of the approximations might be fruitfully increased or decreased in the course of the optimization iterations. The approach is quite general. We make no assumptions on the structure of the original problem, in particular, no assumptions of convexity and separability, and place only mild requirements on the approximations. The approximations used in the framework can be of any nature appropriate to an application; for instance, they can be represented by analyses, simulations, or simple algebraic models. This paper introduces the approach and outlines the convergence analysis.read more
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Proceedings ArticleDOI
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References
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Book
Numerical Methods for Unconstrained Optimization and Nonlinear Equations (Classics in Applied Mathematics, 16)
TL;DR: In this paper, Schnabel proposed a modular system of algorithms for unconstrained minimization and nonlinear equations, based on Newton's method for solving one equation in one unknown convergence of sequences of real numbers.
Book
Numerical methods for unconstrained optimization and nonlinear equations
TL;DR: Newton's Method for Nonlinear Equations and Unconstrained Minimization and methods for solving nonlinear least-squares problems with Special Structure.
Journal ArticleDOI
Approximation concepts for optimum structural design — a review
TL;DR: It is shown that, although the lack of comparative data established on reference test cases prevents an accurate assessment, there have been significant improvements in approximation concepts since the introduction of approximation concepts in the mid-seventies.
Journal ArticleDOI
Some Approximation Concepts for Structural Synthesis
Lucien A. Schmit,B. Farshi +1 more
TL;DR: In this paper, an efficient automated minimum weight design procedure is presented which is applicable to sizing structural systems that can be idealized by truss, shear panel, and constant strain triangles.