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Titlebook: Continuous Optimization; Current Trends and M Vaithilingam Jeyakumar,Alexander Rubinov Book 2005 Springer-Verlag US 2005 Newton‘s method.an

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发表于 2025-3-21 16:12:25 | 显示全部楼层 |阅读模式
书目名称Continuous Optimization
副标题Current Trends and M
编辑Vaithilingam Jeyakumar,Alexander Rubinov
视频video
概述A research contributed volume presenting substantive survey articles in a number of important topic areas of continuous optimization.Contains timely research articles in optimization theory, and numer
丛书名称Applied Optimization
图书封面Titlebook: Continuous Optimization; Current Trends and M Vaithilingam Jeyakumar,Alexander Rubinov Book 2005 Springer-Verlag US 2005 Newton‘s method.an
描述Continuous optimization is the study of problems in which we wish to opti­ mize (either maximize or minimize) a continuous function (usually of several variables) often subject to a collection of restrictions on these variables. It has its foundation in the development of calculus by Newton and Leibniz in the 17*^ century. Nowadys, continuous optimization problems are widespread in the mathematical modelling of real world systems for a very broad range of applications. Solution methods for large multivariable constrained continuous optimiza­ tion problems using computers began with the work of Dantzig in the late 1940s on the simplex method for linear programming problems. Recent re­ search in continuous optimization has produced a variety of theoretical devel­ opments, solution methods and new areas of applications. It is impossible to give a full account of the current trends and modern applications of contin­ uous optimization. It is our intention to present a number of topics in order to show the spectrum of current research activities and the development of numerical methods and applications.
出版日期Book 2005
关键词Newton‘s method; analysis; linear optimization; model; modeling; nonlinear optimization; numerical methods
版次1
doihttps://doi.org/10.1007/b137941
isbn_softcover978-1-4419-3894-7
isbn_ebook978-0-387-26771-5Series ISSN 1384-6485
issn_series 1384-6485
copyrightSpringer-Verlag US 2005
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Some Theoretical Aspects of Newton’s Method for Constrained Best Interpolationx best interpolation problem. Issues addressed include theoretical reduction of the problem to a system of nonsmooth equations, nonsmooth analysis of those equations and development of Newton’s method, convergence analysis and globalization. We frequently use the convex best interpolation to illustr
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On Complexity of Stochastic Programming Problemsing problems with recourse can be solved with a reasonable accuracy by using Monte Carlo sampling techniques, while multistage stochastic programs, in general, are intractable. We also discuss complexity of chance constrained problems and multistage stochastic programs with linear decision rules.
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A Review of Applications of the Cutting Angle Methodsds have recently emerged as a tool for global optimization of families of abstract convex functions. Their applicability have been subsequently extended to other problems, such as scattered data interpolation. This paper reviews three different applications of cutting angle methods, namely global op
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A Numerical Method for Concave Programming Problemsblems have a diverse range of direct and indirect applications. Moreover, concave minimization problems are well known to be NP-hard. In this paper, we present three algorithms which are similar to each other for concave minimization problems. In each iteration of the algorithms, linear programming
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Convexification and Monotone Optimizationence of multiple local optimal solutions, finding a global optimal solution of such a problem is computationally difficult. In this survey paper, we summarize global solution methods for the monotone optimization problem. In particular, we propose a unified framework for the recent progress on conve
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Generalized Lagrange Multipliers for Nonconvex Directionally Differentiable Programsnditions of Kuhn-Tucker type based on the directional derivatives are proved. Here the Lagrange multipliers generally depend on the directions. It is shown that for various concrete classes of problems (including classes convex problems, locally Lipschitz problems, composite nonsmooth problems), gen
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