This book provides a clear, modern, and applicationdriven introduction to mathematical optimizationone of the central technologies underlying today's datadriven decision making. Designed for students and practitioners encountering optimization for the first time, the book develops core concepts through intuitive explanations, concrete examples, and algorithmic insights, while maintaining mathematical rigor where it matters.

Beginning with smooth unconstrained problems, the text builds a unified framework connecting calculus, convexity, and optimality conditions. It progresses naturally to constrained and nonsmooth optimization, introducing subgradients, normal cones, and the KarushKuhnTucker condition in an accessible and coherent manner. Along the way, readers learn how fundamental algorithmssuch as gradient, Newton's, and simplex methodsemerge from the underlying theory and how they behave in practice.

The book places strong emphasis on modeling, guiding readers from realworld problems to optimization formulations and solution strategies. Topics include linear and quadratic programming, network and integer structures, and optimization under uncertainty. Applications are drawn from engineering, operations research, data science, machine learning, and analytics, illustrating how optimization serves as a unifying language across disciplines.

Written as lecture notes for a onesemester introductory course, this book assumes only basic knowledge of calculus and linear algebra. It builds intuition, vocabulary, and mathematical comprehension, while largely avoiding formal proofs. Numerous worked examples, exercises, and fully solved problems support selfstudy and classroom use.

This book is ideal for advanced undergraduate students, master's students, and practitioners seeking a principled yet approachable introduction to optimization, as well as a foundation for further study in applied mathematics, operations research, and analytics.

Connects elementary calculus to the celebrated KKT condition and more general characterization of optimality Stresses sensitivity analysis as the origin of dual problems Large number of worked out examples and exercises

Autorentext

Dr. Johannes O. Royset is professor in the Daniel J. Epstein Department, University of Southern California. He was awarded a National Research Council postdoctoral fellowship in 2003, a Young Investigator Award from the Air Force Office of Scientific Research in 2007, and the Barchi Prize as well as the MOR Journal Award from the Military Operations Research Society in 2009. He received the Goodeve Medal from the Operational Research Society in 2019. Professor Royset was a plenary speaker at the International Conference on Stochastic Programming in 2016, the SIAM Conference on Uncertainty Quantification in 2018, and the INFORMS Security Conference in 2022. He has a PhD from UC Berkeley (2002). Professor Royset has been an associate or guest editor of several journals including SIAM Journal on Optimization, Operations Research, and Mathematical Programming. He has published two books and more than 100 articles.

Inhalt

1 The Optimization Landscape.- 2 Hitting a Wall: Constraints and Nonsmoothness.- 3 Overcoming Uncertainty.- 4 Special Structures: Integers and Networks.- 5 Changing It Up: Perturbation and Duality.- A Solutions to Exercises.- References.- Index.