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Numerical methods for unconstrained optimization and nonlinear equations
  • J. Dennis, B. Schnabel
  • Mathematics, Computer Science
  • Prentice Hall series in computational mathematics
  • 1 March 1983
Preface 1. Introduction. Problems to be considered Characteristics of 'real-world' problems Finite-precision arithmetic and measurement of error Exercises 2. Nonlinear Problems in One Variable. WhatExpand
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Normal-Boundary Intersection: A New Method for Generating the Pareto Surface in Nonlinear Multicriteria Optimization Problems
This paper proposes an alternate method for finding several Pareto optimal points for a general nonlinear multicriteria optimization problem. Such points collectively capture the trade-off among theExpand
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Mesh Adaptive Direct Search Algorithms for Constrained Optimization
This paper addresses the problem of minimization of a nonsmooth function under general nonsmooth constraints when no derivatives of the objective or constraint functions are available. We introduceExpand
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A closer look at drawbacks of minimizing weighted sums of objectives for Pareto set generation in multicriteria optimization problems
A standard technique for generating the Pareto set in multicriteria optimization problems is to minimize (convex) weighted sums of the different objectives for various different settings of theExpand
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Analysis of Generalized Pattern Searches
This paper contains a new convergence analysis for the Lewis and Torczon generalized pattern search (GPS) class of methods for unconstrained and linearly constrained optimization. This analysis isExpand
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A Characterization of Superlinear Convergence and its Application to Quasi-Newton Methods
Let F be a mapping from real n-dimensional Euclidean space into itself. Most practical algorithms for finding a zero of F are of the form $x_{k+1} = x_{k} B_{k}^{-1_{Fx_{k}}}$ where $\{B_{k}\}$ is aExpand
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Problem Formulation for Multidisciplinary Optimization
This paper is about multidisciplinary (design) optimization, or MDO, the coupling of two or more analysis disciplines with numerical optimization.The paper has three goals. First, it is an expositoryExpand
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Quasi-Newton Methods, Motivation and Theory
This paper is an attempt to motivate and justify quasi-Newton methods as useful modifications of Newton''s method for general and gradient nonlinear systems of equations. References are given toExpand
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An Adaptive Nonlinear Least Square Algorithm
NL2SOL is a modular program for solving the nonlinear least-squares problem that incorporates a number of novel features. It maintains a secant approximation S to the second-order part of theExpand
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