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July 8, 2025, 8:35 a.m.
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SOURCE: Haviv M. Continuous Optimization for Data Science 2025
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COVER
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MEDIAINFO
Textbook in PDF format
The text is divided into three main parts: unconstrained optimization, constrained optimization, and linear programming. The first part addresses unconstrained optimization in single-variable and multivariable functions, introducing key algorithms such as steepest descent, Newton, and quasi-Newton methods. The second part focuses on constrained optimization, starting with linear equality constraints and extending to more general cases, including inequality constraints. It details optimality conditions, sensitivity analysis, and relevant algorithms for solving these problems. The third part covers linear programming, presenting the formulation of LP problems, the simplex algorithm, and sensitivity analysis. Throughout, the text provides numerous applications to Data Science, such as linear regression, maximum likelihood estimation, expectation-maximization algorithms, support vector machines, and linear neural networks.
Continuous optimization, sometimes referred to as nonlinear programming (NLP), is an old topic that deals with optimizing continuous functions. It has two main branches: unconstrained and constrained optimization. This text presents both theory and algorithms for solving such problems. Both branches are now more popular than ever and are being used in statistics, Data Science, and Machine Learning. Indeed, many of the examples given in the text are from the theory of statistics.
The text is suitable for third-year bachelor and first-year master students in statistics and Data Science, Computer Science, operations research, engineering, and mathematics. I believe that anyone who is interested in optimization should acquire the material given in the text. For those who wish to specialize in NLP, it can be used mainly as an introductory text, prior to moving to more advanced and more detailed texts.
Preface
PartI: Unconstrained Optimization
Single-Variable Optimization
Multi-Variable Unconstrained Optimization
PartII: Constrained Optimization
Optimization Under Equality Constraints: Special Cases
Optimization Under Equality Constraints: The General Case
Optimization Under Equality and Inequality Constraints
PartIII: Linear Programming
Introduction and Examples
The Simplex Method
Sensitivity Analysis
Solutions to Exercises
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