"A Workbook for Students in a Basic Speech Class"

Organization and Outline

Boyd, Stephen

Pearson College Div

Convex optimization problems arise frequently in many different fields. A comprehensive introduction to the subject, this book shows in detail how such problems can be solved numerically with great efficiency. The focus is on recognizing convex optimization problems and then finding the most appropriate technique for solving them. The text contains many worked examples and homework exercises and will appeal to students, researchers and practitioners in fields such as engineering, computer science, mathematics, statistics, finance, and economics.

Convex Optimization

Science & Math

Vandenberghe, Lieven

Mathematics

Cambridge University Press

Life Class: The Academic Male Nude 1820-1920

LUCIE-SMITH, Edward

Arts & Photography

Heretic Books

Introduction to Applied Linear Algebra: Vectors, Matrices, and Least Squares

This groundbreaking textbook combines straightforward explanations with a wealth of practical examples to offer an innovative approach to teaching linear algebra. Requiring no prior knowledge of the subject, it covers the aspects of linear algebra - vectors, matrices, and least squares - that are needed for engineering applications, discussing examples across data science, machine learning and artificial intelligence, signal and image processing, tomography, navigation, control, and finance. The numerous practical exercises throughout allow students to test their understanding and translate their knowledge into solving real-world problems, with lecture slides, additional computational exercises in Julia and MATLAB®, and data sets accompanying the book online. Suitable for both one-semester and one-quarter courses, as well as self-study, this self-contained text provides beginning students with the foundation they need to progress to more advanced study.

Many problems of recent interest in statistics and machine learning can be posed in the framework of convex optimization. Due to the explosion in size and complexity of modern datasets, it is increasingly important to be able to solve problems with a very large number of features or training examples. As a result, both the decentralized collection or storage of these datasets as well as accompanying distributed solution methods are either necessary or at least highly desirable. Distributed Optimization and Statistical Learning via the Alternating Direction Method of Multipliers argues that the alternating direction method of multipliers is well suited to distributed convex optimization, and in particular to large-scale problems arising in statistics, machine learning, and related areas. The method was developed in the 1970s, with roots in the 1950s, and is equivalent or closely related to many other algorithms, such as dual decomposition, the method of multipliers, Douglas-Rachford splitting, Spingarn's method of partial inverses, Dykstra's alternating projections, Bregman iterative algorithms for ℓ1 problems, proximal methods, and others. After briefly surveying the theory and history of the algorithm, it discusses applications to a wide variety of statistical and machine learning problems of recent interest, including the lasso, sparse logistic regression, basis pursuit, covariance selection, support vector machines, and many others. It also discusses general distributed optimization, extensions to the nonconvex setting, and efficient implementation, including some details on distributed MPI and Hadoop MapReduce implementations

Distributed Optimization and Statistical Learning Via the Alternating Direction Method of Multipliers (Foundations and Trends(r) in Machine Learning)

Computers & Technology

Eckstein, Jonathan

Parikh, Neal

Chu, Eric

Peleato, Borja

Computer Science

Now Publishers

Performance Bounds and Suboptimal Policies for Multi-Period Investment examines dynamic trading of a portfolio of assets in discrete periods over a finite time horizon, with arbitrary time-varying distribution of asset returns. The goal is to maximize the total expected revenue from the portfolio, while respecting constraints on the portfolio like a required terminal portfolio and leverage and risk limits. The revenue takes into account the gross cash generated in trades, transaction costs, and costs associated with the positions, such as fees for holding short positions. The model that is presented takes the form of a stochastic control problem with linear dynamics and convex cost function and constraints. While this problem can be tractably solved in several special cases - for example, when all costs are convex quadratic, or when there are no transaction costs - the focus is on the more general case, with nonquadratic cost terms and transaction costs. Performance Bounds and Suboptimal Policies for Multi-Period Investment shows how to use linear matrix inequality techniques and semidefinite programming to produce a quadratic bound on the value function, which in turn gives a bound on the optimal performance. This performance bound can be used to judge the performance obtained by any suboptimal policy. As a by-product of the performance bound computation, an approximate dynamic programming policy is obtained that requires the solution of a convex optimization problem, often a quadratic program, to determine the trades to carry out in each step.

Performance Bounds and Suboptimal Policies for Multi-Period Investment (Foundations and Trends(r) in Optimization)

汪洋

Mueller, Mark T

Donoghue, Brendan

Proximal Algorithms discusses proximal operators and proximal algorithms, and illustrates their applicability to standard and distributed convex optimization in general and many applications of recent interest in particular. Much like Newton's method is a standard tool for solving unconstrained smooth optimization problems of modest size, proximal algorithms can be viewed as an analogous tool for nonsmooth, constrained, large-scale, or distributed versions of these problems. They are very generally applicable, but are especially well-suited to problems of substantial recent interest involving large or high-dimensional datasets. Proximal methods sit at a higher level of abstraction than classical algorithms like Newton's method: the base operation is evaluating the proximal operator of a function, which itself involves solving a small convex optimization problem. These subproblems, which generalize the problem of projecting a point onto a convex set, often admit closed-form solutions or can be solved very quickly with standard or simple specialized methods. Proximal Algorithms discusses different interpretations of proximal operators and algorithms, looks at their connections to many other topics in optimization and applied mathematics, surveys some popular algorithms, and provides a large number of examples of proximal operators that commonly arise in practice.

Proximal Algorithms (Foundations and Trends(r) in Optimization)

Multi-Period Trading via Convex Optimization considers a basic model of multi-period trading, which can be used to evaluate the performance of a trading strategy. It describes a framework for single-period optimization, where the trades in each period are found by solving a convex optimization problem that trades oﬀ expected return, risk, transaction cost and holding cost such as the borrowing cost for shorting assets. It then describes a multi-period version of the trading method, where optimization is used to plan a sequence of trades, with only the ﬁrst one executed, using estimates of future quantities that are unknown when the trades are chosen. The single period method traces back to Markowitz; the multi-period methods trace back to model predictive control. This monograph addresses the single-period and multi-period methods in one simple framework, giving a clear description of the development and the approximations made. The methods described can be thought of as good ways to exploit predictions, no matter how they are made. We have also developed a companion open-source software library that implements many of the ideas and methods described in the paper.
Multi-Period Trading via Convex Optimization collects in one place the basic deﬁnitions, a careful description of the model, and discussion of how convex optimization can be used in multi-period trading, all in a common notation and framework. It provides the reader with a uniﬁed, self-contained treatment, focusing on the practical issues that arise in multi-period trading. It will benefit anyone interested in the study of these methods and is also an ideal reference for a quantitative trader, or someone who works with or for, or employs, one.

Multi-Period Trading Via Convex Optimization (Foundations and Trends(r) in Optimization)

Busseti, Enzo

Diamond, Steven

Kahn, Ronald N.

Koh, Kwangmoo

Nystrup, Peter

Speth, Jan

Minimum-Distortion Embedding (Foundations and Trends(r) in Machine Learning)

Agrawal, Akshay

Ali, Alnur

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