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Sequential Quadratic Programming
Paul T. Boggs,Jon W. Tolle +1 more
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Since its popularization in the late 1970s, Sequential Quadratic Programming (SQP) has arguably become the most successful method for solving nonlinearly constrained optimization problems.Abstract:
Since its popularization in the late 1970s, Sequential Quadratic Programming (SQP) has arguably become the most successful method for solving nonlinearly constrained optimization problems. As with most optimization methods, SQP is not a single algorithm, but rather a conceptual method from which numerous specific algorithms have evolved. Backed by a solid theoretical and computational foundation, both commercial and public-domain SQP algorithms have been developed and used to solve a remarkably large set of important practical problems. Recently large-scale versions have been devised and tested with promising results.read more
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Numerical Optimization
Jorge Nocedal,Stephen J. Wright +1 more
TL;DR: Numerical Optimization presents a comprehensive and up-to-date description of the most effective methods in continuous optimization, responding to the growing interest in optimization in engineering, science, and business by focusing on the methods that are best suited to practical problems.
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SNOPT: An SQP Algorithm for Large-Scale Constrained Optimization
TL;DR: An SQP algorithm that uses a smooth augmented Lagrangian merit function and makes explicit provision for infeasibility in the original problem and the QP subproblems is discussed.
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The Geometry of Algorithms with Orthogonality Constraints
TL;DR: The theory proposed here provides a taxonomy for numerical linear algebra algorithms that provide a top level mathematical view of previously unrelated algorithms and developers of new algorithms and perturbation theories will benefit from the theory.
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An Interior Point Algorithm for Large-Scale Nonlinear Programming
TL;DR: The design and implementation of a new algorithm for solving large nonlinear programming problems follows a barrier approach that employs sequential quadratic programming and trust regions to solve the subproblems occurring in the iteration.
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AUV Navigation and Localization: A Review
TL;DR: A review of the state of the art of AUV navigation and localization, as well as a description of some of the more commonly used methods, are presented and areas of future research potential are highlighted.
References
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Book
Iterative Solution of Nonlinear Equations in Several Variables
J.M. Ortega,Werner C. Rheinboldt +1 more
TL;DR: In this article, the authors present a list of basic reference books for convergence of Minimization Methods in linear algebra and linear algebra with a focus on convergence under partial ordering.
Book
Practical Methods of Optimization
TL;DR: The aim of this book is to provide a Discussion of Constrained Optimization and its Applications to Linear Programming and Other Optimization Problems.
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.