Lectures on Convex Optimization
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Beschreibung
This book provides a comprehensive, modern introduction to convex optimization, a field that is becoming increasingly important in applied mathematics, economics and finance, engineering, and computer science, notably in data science and machine learning.
Written by a leading expert in the field, this book includes recent advances in the algorithmic theory of convex optimization, naturally complementing the existing literature. It contains a unified and rigorous presentation of the acceleration techniques for minimization schemes of first- and second-order. It provides readers with a full treatment of the smoothing technique, which has tremendously extended the abilities of gradient-type methods. Several powerful approaches in structural optimization, including optimization in relative scale and polynomial-time interior-point methods, are also discussed in detail.
Researchers in theoretical optimization as well as professionals working on optimization problems will findthis book very useful. It presents many successful examples of how to develop very fast specialized minimization algorithms. Based on the author’s lectures, it can naturally serve as the basis for introductory and advanced courses in convex optimization for students in engineering, economics, computer science and mathematics.This book provides a comprehensive, modern introduction to convex optimization, a field that is becoming increasingly important in applied mathematics, economics and finance, engineering, and computer science, notably in data science and machine learning.
Written by a leading expert in the field, this book includes recent advances in the algorithmic theory of convex optimization, naturally complementing the existing literature. It contains a unified and rigorous presentation of the acceleration techniques for minimization schemes of first- and second-order. It provides readers with a full treatment of the smoothing technique, which has tremendously extended the abilities of gradient-type methods. Several powerful approaches in structural optimization, including optimization in relative scale and polynomial-time interior-point methods, are also discussed in detail.
Researchers in theoretical optimization as well as professionals working on optimization problems will findthis book very useful. It presents many successful examples of how to develop very fast specialized minimization algorithms. Based on the author’s lectures, it can naturally serve as the basis for introductory and advanced courses in convex optimization for students in engineering, economics, computer science and mathematics.Presents a self-contained description of fast gradient methods Offers the first description in the monographic literature of the modern second-order methods based on cubic regularization Provides a comprehensive treatment of the smoothing technique Develops a new theory of optimization in relative scale
Autor*in
Yurii Nesterov
Themen in »Lectures on Convex Optimization«
complexity complexity theory graphs mathematical programming optimization Fast Gradient Methods Self-Concordant Functions Interior-Point Methods Smoothing Technique Cubic Regularization of Newton Method Optimization in Relative Scale MSC 2010 49M15, 49M29, 49N15, 65K05, 65K10, 90C25, 90C30, 90C46 90C51, 90C52, 90C60 algorithm analysis and problem complexity
Stimmen zu »Lectures on Convex Optimization«
“It is a must-read for both students involved in the operations research programs, as well as the researchers in the area of nonlinear programming, in particular in convex optimization.” (Marcin Anholcer, zbMATH 1427.90003, 2020)
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