Practical Augmented Lagrangian Methods For Constrained Optimization

Author : Ernesto G. Birgin,JosŸ Mario Martinez
Publisher : SIAM
Page : 222 pages
File Size : 47,8 Mb
Release : 2014-04-30
Category : Mathematics
ISBN : 9781611973358

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Practical Augmented Lagrangian Methods for Constrained Optimization by Ernesto G. Birgin,JosŸ Mario Martinez Pdf

This book focuses on Augmented Lagrangian techniques for solving practical constrained optimization problems. The authors rigorously delineate mathematical convergence theory based on sequential optimality conditions and novel constraint qualifications. They also orient the book to practitioners by giving priority to results that provide insight on the practical behavior of algorithms and by providing geometrical and algorithmic interpretations of every mathematical result, and they fully describe a freely available computational package for constrained optimization and illustrate its usefulness with applications.

Author : Ernesto G. Birgin,Josâ Mario Mart_nez
Publisher : SIAM
Page : 220 pages
File Size : 48,8 Mb
Release : 2014-04-30
Category : Mathematics
ISBN : 9781611973365

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Practical Augmented Lagrangian Methods for Constrained Optimization by Ernesto G. Birgin,Josâ Mario Mart_nez Pdf

This book focuses on Augmented Lagrangian techniques for solving practical constrained optimization problems. The authors: rigorously delineate mathematical convergence theory based on sequential optimality conditions and novel constraint qualifications; orient the book to practitioners by giving priority to results that provide insight on the practical behavior of algorithms and by providing geometrical and algorithmic interpretations of every mathematical result; and fully describe a freely available computational package for constrained optimization and illustrate its usefulness with applications.

Author : Dimitri P. Bertsekas
Publisher : Academic Press
Page : 412 pages
File Size : 48,5 Mb
Release : 2014-05-10
Category : Mathematics
ISBN : 9781483260471

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Constrained Optimization and Lagrange Multiplier Methods by Dimitri P. Bertsekas Pdf

Computer Science and Applied Mathematics: Constrained Optimization and Lagrange Multiplier Methods focuses on the advancements in the applications of the Lagrange multiplier methods for constrained minimization. The publication first offers information on the method of multipliers for equality constrained problems and the method of multipliers for inequality constrained and nondifferentiable optimization problems. Discussions focus on approximation procedures for nondifferentiable and ill-conditioned optimization problems; asymptotically exact minimization in the methods of multipliers; duality framework for the method of multipliers; and the quadratic penalty function method. The text then examines exact penalty methods, including nondifferentiable exact penalty functions; linearization algorithms based on nondifferentiable exact penalty functions; differentiable exact penalty functions; and local and global convergence of Lagrangian methods. The book ponders on the nonquadratic penalty functions of convex programming. Topics include large scale separable integer programming problems and the exponential method of multipliers; classes of penalty functions and corresponding methods of multipliers; and convergence analysis of multiplier methods. The text is a valuable reference for mathematicians and researchers interested in the Lagrange multiplier methods.

Author : Philip E. Gill,Walter Murray,Margaret H. Wright
Publisher : Unknown
Page : 428 pages
File Size : 46,7 Mb
Release : 1981
Category : Mathematics
ISBN : UOM:39015016359609

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Practical Optimization by Philip E. Gill,Walter Murray,Margaret H. Wright Pdf

Mathematics of Computing -- Numerical Analysis.

Author : Margaret Ann Hagen Wright
Publisher : Unknown
Page : 552 pages
File Size : 47,8 Mb
Release : 1976
Category : Algorithms
ISBN : STANFORD:36105031717635

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Numerical Methods for Nonlinearly Constrained Optimization by Margaret Ann Hagen Wright Pdf

Author : Robert Michael Lewis,Institute for Computer Applications in Science and Engineering,Virginia Torczon
Publisher : Unknown
Page : 22 pages
File Size : 45,6 Mb
Release : 1998
Category : Electronic
ISBN : NASA:31769000708084

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A Globally Convergent Augmented Lagrangian Pattern Search Algorithm for Optimization with General Constraints and Simple Bounds by Robert Michael Lewis,Institute for Computer Applications in Science and Engineering,Virginia Torczon Pdf

Author : Robert S. Anderssen,Philip Broadbridge,Yasuhide Fukumoto,Kenji Kajiwara,Tsuyoshi Takagi,Evgeny Verbitskiy,Masato Wakayama
Publisher : Springer
Page : 278 pages
File Size : 50,5 Mb
Release : 2015-10-11
Category : Technology & Engineering
ISBN : 9784431553427

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Applications + Practical Conceptualization + Mathematics = fruitful Innovation by Robert S. Anderssen,Philip Broadbridge,Yasuhide Fukumoto,Kenji Kajiwara,Tsuyoshi Takagi,Evgeny Verbitskiy,Masato Wakayama Pdf

This book is a collection of papers presented at the conference “Forum Math-for-Industry 2014” for which the unifying theme was “Applications + Practical Conceptualization + Mathematics = fruitful Innovation” in October 2014. This epigram encapsulates the dynamics of the process that takes an application through to an innovation. Industrial mathematics can be viewed as the causal engine that implements the epigram by taking an Application such as input and convolving it with a mixture of Practical Conceptualization and Mathematics to generate a fruitful Innovation as output. The book illustrates various aspects of the two-way interaction between applications and their association highlighting how practical conceptualization assists with the linking of the question that encapsulates the current application to the relevant mathematics. The contents of this volume address productive and successful interaction between industry and mathematicians, as well as the cross-fertilization and collaboration that result when mathematics is involved with the advancement of science and technology.

Author : Stanford University. Systems Optimization Laboratory
Publisher : Unknown
Page : 48 pages
File Size : 50,7 Mb
Release : 1979
Category : Electronic
ISBN : STANFORD:36105046361965

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Algorithms for Nonlinearly Constrained Optimization by Stanford University. Systems Optimization Laboratory Pdf

Author : Coralia Cartis,Nicholas I. M. Gould,Philippe L. Toint
Publisher : SIAM
Page : 549 pages
File Size : 47,7 Mb
Release : 2022-07-06
Category : Mathematics
ISBN : 9781611976991

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Evaluation Complexity of Algorithms for Nonconvex Optimization by Coralia Cartis,Nicholas I. M. Gould,Philippe L. Toint Pdf

A popular way to assess the “effort” needed to solve a problem is to count how many evaluations of the problem functions (and their derivatives) are required. In many cases, this is often the dominating computational cost. Given an optimization problem satisfying reasonable assumptions—and given access to problem-function values and derivatives of various degrees—how many evaluations might be required to approximately solve the problem? Evaluation Complexity of Algorithms for Nonconvex Optimization: Theory, Computation, and Perspectives addresses this question for nonconvex optimization problems, those that may have local minimizers and appear most often in practice. This is the first book on complexity to cover topics such as composite and constrained optimization, derivative-free optimization, subproblem solution, and optimal (lower and sharpness) bounds for nonconvex problems. It is also the first to address the disadvantages of traditional optimality measures and propose useful surrogates leading to algorithms that compute approximate high-order critical points, and to compare traditional and new methods, highlighting the advantages of the latter from a complexity point of view. This is the go-to book for those interested in solving nonconvex optimization problems. It is suitable for advanced undergraduate and graduate students in courses on advanced numerical analysis, data science, numerical optimization, and approximation theory.

Author : Carlile Lavor,Francisco A. M. Gomes
Publisher : Springer
Page : 407 pages
File Size : 44,9 Mb
Release : 2018-09-07
Category : Mathematics
ISBN : 9783319940151

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Advances in Mathematics and Applications by Carlile Lavor,Francisco A. M. Gomes Pdf

This book celebrates the 50th anniversary of the Institute of Mathematics, Statistics and Scientific Computing (IMECC) of the University of Campinas, Brazil, by offering reviews of selected research developed at one of the most prestigious mathematics institutes in Latin America. Written by senior professors at the IMECC, it covers topics in pure and applied mathematics and statistics ranging from differential geometry, dynamical systems, Lie groups, and partial differential equations to computational optimization, mathematical physics, stochastic process, time series, and more. A report on the challenges and opportunities of research in applied mathematics - a highly active field of research in the country - and highlights of the Institute since its foundation in 1968 completes this historical volume, which is unveiled in the same year that the International Mathematical Union (IMU) names Brazil as a member of the Group V of countries with the most relevant contributions in mathematics.

Author : Ritu Arora,Shalini Arora,Anand J Kulkarni,Patrick Siarry
Publisher : CRC Press
Page : 184 pages
File Size : 40,9 Mb
Release : 2023-05-12
Category : Business & Economics
ISBN : 9781000859850

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Combinatorial Optimization Under Uncertainty by Ritu Arora,Shalini Arora,Anand J Kulkarni,Patrick Siarry Pdf

This book discusses the basic ideas, underlying principles, mathematical formulations, analysis and applications of the different combinatorial problems under uncertainty and attempts to provide solutions for the same. Uncertainty influences the behaviour of the market to a great extent. Global pandemics and calamities are other factors which affect and augment unpredictability in the market. The intent of this book is to develop mathematical structures for different aspects of allocation problems depicting real life scenarios. The novel methods which are incorporated in practical scenarios under uncertain circumstances include the STAR heuristic approach, Matrix geometric method, Ranking function and Pythagorean fuzzy numbers, to name a few. Distinct problems which are considered in this book under uncertainty include scheduling, cyclic bottleneck assignment problem, bilevel transportation problem, multi-index transportation problem, retrial queuing, uncertain matrix games, optimal production evaluation of cotton in different soil and water conditions, the healthcare sector, intuitionistic fuzzy quadratic programming problem, and multi-objective optimization problem. This book may serve as a valuable reference for researchers working in the domain of optimization for solving combinatorial problems under uncertainty. The contributions of this book may further help to explore new avenues leading toward multidisciplinary research discussions.

Author : Michael Hintermüller,Roland Herzog,Christian Kanzow,Michael Ulbrich,Stefan Ulbrich
Publisher : Springer Nature
Page : 518 pages
File Size : 46,8 Mb
Release : 2022-02-18
Category : Mathematics
ISBN : 9783030793937

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Non-Smooth and Complementarity-Based Distributed Parameter Systems by Michael Hintermüller,Roland Herzog,Christian Kanzow,Michael Ulbrich,Stefan Ulbrich Pdf

Many of the most challenging problems in the applied sciences involve non-differentiable structures as well as partial differential operators, thus leading to non-smooth distributed parameter systems. This edited volume aims to establish a theoretical and numerical foundation and develop new algorithmic paradigms for the treatment of non-smooth phenomena and associated parameter influences. Other goals include the realization and further advancement of these concepts in the context of robust and hierarchical optimization, partial differential games, and nonlinear partial differential complementarity problems, as well as their validation in the context of complex applications. Areas for which applications are considered include optimal control of multiphase fluids and of superconductors, image processing, thermoforming, and the formation of rivers and networks. Chapters are written by leading researchers and present results obtained in the first funding phase of the DFG Special Priority Program on Nonsmooth and Complementarity Based Distributed Parameter Systems: Simulation and Hierarchical Optimization that ran from 2016 to 2019.

Author : M. Fortin,R. Glowinski
Publisher : Elsevier
Page : 339 pages
File Size : 45,7 Mb
Release : 2000-04-01
Category : Mathematics
ISBN : 008087536X

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Augmented Lagrangian Methods by M. Fortin,R. Glowinski Pdf

The purpose of this volume is to present the principles of the Augmented Lagrangian Method, together with numerous applications of this method to the numerical solution of boundary-value problems for partial differential equations or inequalities arising in Mathematical Physics, in the Mechanics of Continuous Media and in the Engineering Sciences.

Author : Jinyang Liang
Publisher : Springer Nature
Page : 697 pages
File Size : 40,6 Mb
Release : 2024-05-13
Category : Electronic
ISBN : 9783031390623

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Coded Optical Imaging by Jinyang Liang Pdf

Author : Emmanuel Trélat,Enrique Zuazua
Publisher : Elsevier
Page : 662 pages
File Size : 52,5 Mb
Release : 2023-02-20
Category : Mathematics
ISBN : 9780323858267

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Numerical Control: Part B by Emmanuel Trélat,Enrique Zuazua Pdf

Numerical Control: Part B, Volume 24 in the Handbook of Numerical Analysis series, highlights new advances in the field, with this new volume presenting interesting chapters written by an international board of authors. Chapters in this volume include Control problems in the coefficients and the domain for linear elliptic equations, Computational approaches for extremal geometric eigenvalue problems, Non-overlapping domain decomposition in space and time for PDE-constrained optimal control problems on networks, Feedback Control of Time-dependent Nonlinear PDEs with Applications in Fluid Dynamics, Stabilization of the Navier-Stokes equations - Theoretical and numerical aspects, Reconstruction algorithms based on Carleman estimates, and more. Other sections cover Discrete time formulations as time discretization strategies in data assimilation, Back and forth iterations/Time reversal methods, Unbalanced Optimal Transport: from Theory to Numerics, An ADMM Approach to the Exact and Approximate Controllability of Parabolic Equations, Nonlocal balance laws -- an overview over recent results, Numerics and control of conservation laws, Numerical approaches for simulation and control of superconducting quantum circuits, and much more. Provides the authority and expertise of leading contributors from an international board of authors Presents the latest release in the Handbook of Numerical Analysis series Updated release includes the latest information on Numerical Control