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About 10,000 papers for “Convex optimization”

Convex optimization

Ruud, Arto · CERN Document Server (European Organization for Nuclear Research) · 2019

Cited by 0

Convex Optimization

Ali H. Sayed · Cambridge University Press eBooks · 2022

This extraordinary three-volume work, written in an engaging and rigorous style by a world authority in the field, provides an accessible, comprehensive introduction to the full spectrum of mathematical and statistical techniques underpinning contemporary methods in data-driven learning and inference. This first volume, Foundations, introduces core topics in inference and learning, such as matrix theory, linear algebra, random variables, convex optimization and stochastic optimization, and prepares students for studying their practical application in later volumes. A consistent structure and pedagogy is employed throughout this volume to reinforce student understanding, with over 600 end-of-chapter problems (including solutions for instructors), 100 figures, 180 solved examples, datasets and downloadable Matlab code. Supported by sister volumes Inference and Learning, and unique in its scale and depth, this textbook sequence is ideal for early-career researchers and graduate students across many courses in signal processing, machine learning, statistical analysis, data science and inference.

Cited by 0

Convex Optimization

Vivek S. Borkar, K. S. Mallikarjuna Rao · Texts and readings in mathematics · 2023

Cited by 0

Convex Optimization

Stephen Boyd, Lieven Vandenberghe · Cambridge University Press eBooks · 2004

Convex optimization problems arise frequently in many different fields. This book provides a comprehensive introduction to the subject, and shows in detail how such problems can be solved numerically with great efficiency. The book begins with the basic elements of convex sets and functions, and then describes various classes of convex optimization problems. Duality and approximation techniques are then covered, as are statistical estimation techniques. Various geometrical problems are then presented, and there is detailed discussion of unconstrained and constrained minimization problems, and interior-point methods. The focus of the book is on recognizing convex optimization problems and then finding the most appropriate technique for solving them. It 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.

Cited by 31,091Open access

Convex Optimization

Kenneth J. Winston · Cambridge University Press eBooks · 2023

A comprehensive modern introduction to risk and portfolio management for quantitatively adept advanced undergraduate and beginning graduate students who will become practitioners in the field of quantitative finance. With a focus on real-world application, but providing a background in academic theory, this text builds a firm foundation of rigorous but practical knowledge. Extensive live data and Python code are provided as online supplements, allowing a thorough understanding of how to manage risk and portfolios in practice. With its detailed examination of how mathematical techniques are applied to finance, this is the ideal textbook for giving students with a background in engineering, mathematics or physics a route into the field of quantitative finance.

Cited by 0

Convex Optimization

Abner J. Salgado, Steven M. Wise · Cambridge University Press eBooks · 2022

This chapter serves two purposes: it introduces several essential concepts of linear and nonlinear functional analysis that will be used in subsequent chapters and, as an illustration of them, studies the problem of unconstrained minimization of a convex functional. All the necessary notions of existence, uniqueness, and optimality conditions are presented and analyzed. Preconditioned gradient descent methods for strongly convex, locally Lipschitz smooth objectives in infinite dimensions are then presented and analyzed. A general framework to show linear convergence in this setting is then presented. The preconditioned steepest descent with exact and approximate line searches are then analyzed using the same framework. Finally, the application of Newton’s method to the Euler equations is discussed. The local convergence is shown, and how to achieve global convergence is briefly discussed.

Cited by 0

Convex Optimization

Francisco J. Aragón, Miguel Á. Goberna, Marco A. López et al. · Springer undergraduate texts in mathematics and technology · 2019

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Convex Optimization

Krzysztof Postek, Alessandro Zocca, Joaquim A. S. Gromicho et al. · Cambridge University Press eBooks · 2025

This practical guide to optimization combines mathematical theory with hands-on coding examples to explore how Python can be used to model problems and obtain the best possible solutions. Presenting a balance of theory and practical applications, it is the ideal resource for upper-undergraduate and graduate students in applied mathematics, data science, business, industrial engineering and operations research, as well as practitioners in related fields. Beginning with an introduction to the concept of optimization, this text presents the key ingredients of an optimization problem and the choices one needs to make when modeling a real-life problem mathematically. Topics covered range from linear and network optimization to convex optimization and optimizations under uncertainty. The book's Python code snippets, alongside more than 50 Jupyter notebooks on the author's GitHub, allow students to put the theory into practice and solve problems inspired by real-life challenges, while numerous exercises sharpen students' understanding of the methods discussed.

Cited by 0

Convex Optimization

Emilie March, Ise Jean-françois, Remacle Christophe Geuzaine · 2004

Cited by 0

Are Convex Optimization Curves Convex?

Barzilai, Guy, Shamir, Ohad, Zamani, Moslem · ArXiv.org · 2025

In this paper, we study when we might expect the optimization curve induced by gradient descent to be \emph{convex} -- precluding, for example, an initial plateau followed by a sharp decrease, making it difficult to decide when optimization should stop. Although such undesirable behavior can certainly occur when optimizing general functions, might it also occur in the benign and well-studied case of smooth convex functions? As far as we know, this question has not been tackled in previous work. We show, perhaps surprisingly, that the answer crucially depends on the choice of the step size. In particular, for the range of step sizes which are known to result in monotonic convergence to an optimal value, we characterize a regime where the optimization curve will be provably convex, and a regime where the curve can be non-convex. We also extend our results to gradient flow, and to the closely-related but different question of whether the gradient norm decreases monotonically.

Cited by 0Open access

Are Convex Optimization Curves Convex?

Barzilai, Guy, Shamir, Ohad, Zamani, Moslem · arXiv (Cornell University) · 2025

In this paper, we study when we might expect the optimization curve induced by gradient descent to be \emph{convex} -- precluding, for example, an initial plateau followed by a sharp decrease, making it difficult to decide when optimization should stop. Although such undesirable behavior can certainly occur when optimizing general functions, might it also occur in the benign and well-studied case of smooth convex functions? As far as we know, this question has not been tackled in previous work. We show, perhaps surprisingly, that the answer crucially depends on the choice of the step size. In particular, for the range of step sizes which are known to result in monotonic convergence to an optimal value, we characterize a regime where the optimization curve will be provably convex, and a regime where the curve can be non-convex. We also extend our results to gradient flow, and to the closely-related but different question of whether the gradient norm decreases monotonically.

Cited by 0Open access

Convex Optimization Overview

Zico Kolter, Honglak Lee · 2008

1 Introduction Many situations arise in machine learning where we would like to optimize the value of some function. That is, given a function f: Rn! R, we want to find x 2 Rn that minimizes (or maximizes) f (x). We have already seen several examples of optimization problems in class: least-squares, logistic regression, and support vector machines can all be framed as optimization problems.

Cited by 0