Practical Nonconvex Nonsmooth Optimization

Frank E. Curtis · Daniel P. Robinson

Dec 2025 · SIAM

Ebook

509

Pages

Eligible

About this ebook

This book provides a clear and accessible introduction to an important class of problems in mathematical optimization: those involving continuous functions that may be nonconvex, nonsmooth, or both. The authors begin with an intuitive treatment of theoretical foundations, including properties of nonconvex and nonsmooth functions and conditions for optimality. They then offer a broad overview of the most effective and efficient algorithms for solving such problems, with a focus on practical applications in areas such as control systems, signal processing, and data science.

Practical Nonconvex Nonsmooth Optimization focuses on problems in finite-dimensional real-vector spaces, avoiding the need for a background in functional analysis. It introduces concepts through nonconvex smooth optimization, making the material more accessible to those without extensive experience in convex analysis. A conversational tone is used throughout, with technical proofs placed at the end of each chapter to help readers understand the core ideas before engaging with detailed arguments.

This book is intended for advanced undergraduates and graduate students who are familiar with basic optimization concepts and are ready to explore more complex problems. A background in calculus, real analysis, linear algebra, and probability is recommended. It is appropriate for an introductory graduate-level course in continuous optimization. Practitioners and early career researchers will also find the book useful.

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About the author

Frank E. Curtis is a professor in the Department of Industrial and Systems Engineering at Lehigh University. He is a recipient of an Early Career Award from the Advanced Scientific Computing Research program of the U.S. Department of Energy, the INFORMS Computing Society Prize, and the SIAM/MOS Lagrange Prize in Continuous Optimization. He is an area editor for Continuous Optimization for the journals Mathematics of Operations Research and Mathematical Programming Computation and an associate editor for several other journals, including Mathematical Programming, SIAM Journal on Optimization, Operations Research, IMA Journal of Numerical Analysis, and INFORMS Journal on Optimization.

Daniel P. Robinson is a professor in the Department of Industrial and Systems Engineering at Lehigh University. He received the Professor Joel Dean Award for Excellence in Teaching from Johns Hopkins University in 2012 and 2018 and a Best Paper Prize from the journal Optimization Letters for his co-authored 2018 paper, “Concise Complexity Analyses for Trust-Region Methods.” He is an associate editor for the journals Computational Optimization and Applications, Optimization Methods and Software, Optimization Letters, and Mathematics of Operations Research. His primary research area is optimization, with a specific focus on the design, analysis, and implementation of efficient algorithms for large-scale convex and nonconvex problems as well as on applications related to computer vision and medicine/healthcare.

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