Introduction to Nonsmooth Analysis and Optimization
2020年1月1日 · This book aims to give an introduction to generalized derivative concepts useful in deriving necessary optimality conditions and numerical algorithms for infinite-dimensional nondifferentiable optimization problems that arise in inverse problems, imaging, and PDE-constrained optimization.
优化 | 非光滑优化的光滑化 - 知乎 - 知乎专栏
本文整理自知乎提问“在你的研究中，非光滑优化(Nonsmooth Optimization)有哪些应用？ ”的两个回答。 第一个回答介绍了什么是Nesterov's smoothing technique，以及它在Packing LP中的应用；第二个回答补充了它在对偶分解中的应用。
非光滑分析 - 百度百科
非凸分析 (nonconvex analysis) 试图把凸分析的基本理论和方法推广到非凸集和非凸函数情形的数学分支.这个名称现今已不常用,而代之为非光滑分析、集值分析等。. 非光滑分析 (nonsmooth analysis) 凸分析的发展.凸分析的次微分理论使得人们能够对非光滑凸函数推广微分 ...
Introduction to Nonsmooth Optimization: Theory, Practice and …
This book is the first easy-to-read text on nonsmooth optimization (NSO, not necessarily differentiable optimization). Solving these kinds of problems plays a critical role in many industrial applications and real-world modeling systems, for example in the context of image denoising, optimal control, neural network training, data mining ...
Instead, nonsmooth optimization typically deals with highly structured problems, but problems which arise differently, or are modeled or cast differently, from ones for which many of the mainline numerical methods, involving gradient vectors and Hessian matri-
Lecture 17: Nonsmooth Optimization Yudong Chen All methods we have seen so far work under the assumption that the objective function f is smooth and in particular differentiable. In this lecture, we consider nonsmooth functions. 1 Nonsmooth optimization Consider the problem min x∈X f(x). (P) Assumptions:
Introduction. Quasi-Newton Methods. Some Difficult Examples. Limited Memory Methods. Concluding Remarks. Nonsmooth, Nonconvex Optimization. Problem: find x that locally minimizes f , where f : R. n → R is. Example Methods Suitable for Nonsmooth Functions Failure of Steepest Descent: Simpler Example. Gradient Sampling. Quasi-Newton Methods.
Nonsmooth Analysis and Control Theory | SpringerLink
In the last decades the subject of nonsmooth analysis has grown rapidly due to the recognition that nondifferentiable phenomena are more widespread, and play a more important role, than had been thought. In recent years, it has come to play a role in functional analysis, optimization, optimal design, mechanics and plasticity, differential ...
Theory of Nonsmooth Optimization | SpringerLink
2020年2月25日 · Nonsmooth optimization (NSO) refers to the general problem of minimizing (or maximizing) functions with discontinuous gradients. These types of problems appear in many applied fields, for example, in image denoising, optimal control, data mining, economics, computational chemistry and physics.
The aim of nonsmooth analysis is therefore to ˙nd generalized derivative concepts that on the one hand allow the above sketched approach for such functions and on the other hand admit a su˝ciently rich calculus to give explicit derivatives for a su˝ciently large class of functions.
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