Cover of: Minimization methods for non-differentiable functions | N. Z. Shor

Minimization methods for non-differentiable functions

  • 4.87 MB
  • English
Springer-Verlag , Berlin, New York
Mathematical optimization., Nondifferentiable funct
StatementN.Z. Shor ; translated from the Russian by K.C. Kiwiel and A. Ruszczyński.
SeriesSpringer series in computational mathematics -- 3
LC ClassificationsQA402.5
ID Numbers
Open LibraryOL22194916M
ISBN 100387127631

Minimization Methods for Non-Differentiable Functions. Authors This monograph summarizes to a certain extent fifteen years of the author's work on developing generalized gradient methods for nonsmooth minimization.

This work started in the department of economic cybernetics of the Institute of Cybernetics of the Ukrainian Academy of.

Methods for minimizing functions with discontinuous gradients are gaining in importance and the ~xperts in the computational methods of mathematical programming tend to agree that progress in the development of algorithms for minimizing nonsmooth functions is the key to the con­ struction of efficient techniques for solving large scale problems.

Reviewer: A. Chris Rolls Newbery This book presents the theory relating to minimization using generalized gradients for nondifferentiable functions. Many standard operations-research problems are considered, and the value of space-dilation is emphasized.

Minimization methods for non-differentiable functions. Berlin ; New York: Springer-Verlag, (OCoLC) Material Type: Internet resource: Document Type: Book, Internet Resource: All Authors / Contributors: Naum Zuselevich Shor. COVID Resources.

Reliable information about the coronavirus (COVID) is available from the World Health Organization (current situation, international travel).Numerous and frequently-updated resource results are available from this Minimization methods for non-differentiable functions book WebJunction has pulled together information and resources to assist library staff as they consider how to handle coronavirus.

Mathematical optimization (alternatively spelt optimisation) or mathematical programming is the selection of a best element (with regard to some criterion) from some set of available alternatives.

Optimization problems of sorts arise in all quantitative disciplines from computer science and engineering to operations research and economics, and the development of solution methods has been of.

Book Title Minimization methods for non-differentiable functions: Author(s) Shor, Naum Zuselevich: Publication Berlin: Springer, - p.

Series (Springer series in computational mathematics; 3) Note Transl. from the Russian, Kiev, Naukova Dumka, Subject code Subject category Mathematical Physics and Mathematics: KeywordsCited by: Home Browse by Title Books Minimization methods for non-differentiable functions.

Minimization methods for non-differentiable functions May May Read More. Authors: N. Shor. The Academy of Sciences of the Ukrainian SSR, Kiev, USSR, Krzysztof C.

Kiwiel. : Minimization Methods for Non-Differentiable Functions and Applications (SPRINGER SERIES IN COMPUTATIONAL MATHEMATICS) (): Shor, Naum Zuselevich: BooksCited by:   Minimization Methods for Non-Differentiable Functions by Naum Z.

Shor,available at Book Depository with free delivery worldwide. Shor, N. Z.: Minimization Methods for Non‐Differentiable Functions. Springer Ser. in Comp. Mathem. 3, Springer‐Verlag, Berlin — Heidelberg — New York Author: D. Rasch. In the case of differentiable, and certain non- differentiable, functions /i/, such a system is for~ed by the unit vectors of a Cartesian system of coordinates in R", which leads to the method of coordinate relaxation.

Questions of the convergence of this method have been well studied, see e.g., /i, 3/.Author: S. Repin. In this paper we propose a new approach for constructing efficient schemes for nonsmooth convex optimization.

It is based on a special smoothing technique, which can be applied to the functions with explicit max-structure. Our approach can be considered as an alternative to black-box minimization.

Minimization Methods for Non-Differentiable Functions In recent years much attention has been given to the development of auto matic systems of planning, design and control in various branches of the national economy.

Quality of decisions is an issue which has come to the forefront, increasing the significance of optimization algorithms in math. Shor N.Z. () Applications of Methods for Nonsmooth Optimization to the Solution of Mathematical Programming Problems.

In: Minimization Methods for Non-Differentiable Functions. Springer Series in Computational Mathematics, vol : Naun Zuselevich Shor.

A method for non-differentiable optimization problems convex minimization.- Methods with subgradient locality measures for minimizing nonconvex functions.- Methods with subgradient deletion Author: Gianfranco Corradi. An energy minimization approach to initially rigid cohesive fracture is proposed, whose key feature is a term for the energy stored in the interfaces that is nondifferentiable at the origin.

Minimization Methods for Non-Differentiable Functions的话题 (全部 条) 什么是话题 无论是一部作品、一个人,还是一件事,都往往可以衍生出许多不同的话题。. The methods to be used for unconstrained minimization of the augmented Lagrangian rely on the continuity of second derivatives.

Details Minimization methods for non-differentiable functions FB2

Multiplier methods corresponding to different types of penalty functions can exhibit different rates of convergence. For functions of more than one variable, differentiability at a point is not equivalent to the existence of the partial derivatives at the point; there are examples of non-differentiable functions that have partial derivatives.

For example, the function. Minimization Methods for Non-Differentiable Functions 英文书摘要. 查看全文信息(Full Text Information) Minimization Methods for Non-Differentiable Functions.

This paper presents a systematic approach for minimization of a wide class of non- differentiable functions. The technique is based on approximation of the nondif- ferentiable function by a smooth function and is related to penalty and multiplier methods for constrained minimization.

Subgradient methods are iterative methods for solving convex minimization problems. Originally developed by Naum Z. Shor and others in the s and s, subgradient methods are convergent when applied even to a non-differentiable objective function.

When the objective function is differentiable, sub-gradient methods for unconstrained problems use the same search direction as the method of. Smoothing methods for nonsmooth, nonconvex minimization 73 Definition 1 Let f: Rn → R be a continuous function.

We call f˜: Rn ×R+ → R a smoothing function of f,iff˜(,μ)is continuously differentiable in Rn for any fixed μ>0, and for any x ∈ Rn, lim z→x,μ↓0 f˜(z,μ)= f (x).

Description Minimization methods for non-differentiable functions FB2

Based on this definition, we can construct a smoothing method using f˜ and ∇x f˜. The Powell's and Brent's methods are ones of the fastest line-search derivative-free optimization methods.

These methods are good for badly scaled differentiable functions. But these methods are very unreliable for non-differentiable functions and for costrained optimization task when extremum point belong to constraint bound. In particular, you might consult the Shor's book "Minimization methods for non-differentiable functions" and Pshnenichnyi's 2 books referenced therein.

Also, Matlab has a function for numerical discontinuous minimization that may be of value. $\endgroup$ – George Kamin Sep 7 '16 at Organizing the topics from general to more specific, the book first gives an overview of sequential optimization, the subclasses of auxiliary-function methods, and the SUMMA algorithms.

The next three chapters present particular examples in more detail, including barrier- and penalty-function methods, proximal minimization, and forward-backward. Generally the most common forms of non-differentiable behavior involve a function going to infinity at x, or having a jump or cusp at x.

There are however stranger things. The function sin(1/x), for example is singular at x = 0 even though it always lies between -1 and 1.

Chapter 9: Numerical Differentiation, and Non-Differentiable Functions. Introduction. We discuss how you can numerically differentiate a function with high accuracy with little effort. One setup can allow you to do so for any function you can enter by doing so once, and doing some then indicate how one can estimate the derivative of.

Operator Splitting Methods in Compressive Sensing and Sparse Approximation 3 min x kxk 1 s.t. kAx bk2 s: (4) See [9] for a discussion of connections between these formulations. In the context of compressive sensing, the measurement matrix A is constructed so that ‘ 1 minimization is capable of stably recovering the sparse signal of inter-est File Size: KB.

The SUMMA Class of AF Methods. Barrier-Function and Penalty-Function Methods Barrier Functions Examples of Barrier Functions Penalty Functions Examples of Penalty Functions Basic Facts.

Proximal Minimization The Basic Problem Proximal Minimization Algorithms Some Obstacles All PMA Are SUMMA Convergence of the PMA The Non-Differentiable Case The IPA.

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If you are adding two functions at a point, you’re just moving up the y-value of one function by the value of the other function. If there are points everywhere for both functions, then there will be points everywhere for the third function.

You can construct trivial cases where they are differentiable: For example, if [math]f(x)[/math] is a non-differentiable function, and [math]g(x) = x - f(x)[/math] is another function, then [math]g(x)[/math] must also be non-differntiable, since d.