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Titlebook: Reformulation: Nonsmooth, Piecewise Smooth, Semismooth and Smoothing Methods; Masao Fukushima,Liqun Qi Book 1999 Springer Science+Business

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书目名称Reformulation: Nonsmooth, Piecewise Smooth, Semismooth and Smoothing Methods
编辑Masao Fukushima,Liqun Qi
视频video
丛书名称Applied Optimization
图书封面Titlebook: Reformulation: Nonsmooth, Piecewise Smooth, Semismooth and Smoothing Methods;  Masao Fukushima,Liqun Qi Book 1999 Springer Science+Business
描述The concept of "reformulation" has long been playing an important role in mathematical programming. A classical example is the penalization technique in constrained optimization that transforms the constraints into the objective function via a penalty function thereby reformulating a constrained problem as an equivalent or approximately equivalent unconstrained problem. More recent trends consist of the reformulation of various mathematical programming prob­ lems, including variational inequalities and complementarity problems, into equivalent systems of possibly nonsmooth, piecewise smooth or semismooth nonlinear equations, or equivalent unconstrained optimization problems that are usually differentiable, but in general not twice differentiable. Because of the recent advent of various tools in nonsmooth analysis, the reformulation approach has become increasingly profound and diversified. In view of growing interests in this active field, we planned to organize a cluster of sessions entitled "Reformulation - Nonsmooth, Piecewise Smooth, Semismooth and Smoothing Methods" in the 16th International Symposium on Mathematical Programming (ismp97) held at Lausanne EPFL, Switzerland on A
出版日期Book 1999
关键词Finite; Operations Research; Operator; Variable; algorithm; algorithms; calculus; equation; function; linear
版次1
doihttps://doi.org/10.1007/978-1-4757-6388-1
isbn_softcover978-1-4419-4805-2
isbn_ebook978-1-4757-6388-1Series ISSN 1384-6485
issn_series 1384-6485
copyrightSpringer Science+Business Media Dordrecht 1999
The information of publication is updating

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1384-6485 technique in constrained optimization that transforms the constraints into the objective function via a penalty function thereby reformulating a constrained problem as an equivalent or approximately equivalent unconstrained problem. More recent trends consist of the reformulation of various mathemat
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Modeling and Solution Environments for MPEC: GAMS & MATLAB,GAMS MPEC model type has been designed using the interface routines. Existing MPEC models from the literature have been written in GAMS, and computational results are given that were obtained using all the tools described.
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Regularized Newton Methods for Minimization of Convex Quadratic Splines with Singular Hessians,ow, we show that one can find a global minimizer of .(.) in finitely many iterations even though the global minimizers of .(.) might form an unbounded set. The new idea is to use a regularized Newton direction when a Hessian matrix of .(.) is singular. Applications to quadratic programming are also included.
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,-Enlargements of Maximal Monotone Operators: Theory and Applications,tablish some theoretical properties of .., including a transportation formula, its Lipschitz continuity, and a result generalizing Brønsted & Rockafellar’s theorem. Then we make use of the .-enlargement to define an algorithm for finding a zero of ..
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