Overview

This book addresses an important class of problems in the field of mathematical optimization­ – those involving nonconvex and/or nonsmooth continuous functions. The authors introduce the theoretical foundations of nonconvex nonsmooth functions and discuss optimality conditions for optimization problems involving such functions. They also provide a wide-ranging review of the foundations underlying the most effective and efficient algorithms for solving nonconvex nonsmooth optimization problems. This challenging class of problems has applications in areas such as control systems, signal processing, and data science. In Practical Nonconvex Nonsmooth Optimization the authors define problems over finite-dimensional real-vector spaces, so readers do not need an extensive background in functional analysis, use nonconvex smooth optimization as a starting point rather than convex optimization, making it easier for those who do not have an extensive background in convex analysis and optimization, and employ a conversational style and put long technical proofs at the end of each chapter so that the main ideas are understood before looking into the details of long, technical proofs.

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9781611978582

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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 journal Mathematics of Operations Research and Associate Editor for Mathematical Programming, SIAM Journal on Optimization, Operations Research, IMA Journal of Numerical Analysis, INFORMS Journal on Optimization, and Mathematical Programming Computation. Daniel P. Robinson joined the Department of Industrial and Systems Engineering in the P.C. Rossin College of Engineering and Applied Science at Lehigh University in 2019. He was awarded the Professor Joel Dean Award for Excellence in Teaching at the Johns Hopkins University in 2012 and 2018 and a Best Paper Prize from 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 specific interest in the design, analysis, and implementation of efficient algorithms for large-scale convex and nonconvex problems, with particular interest in applications related to computer vision and medicine/healthcare.

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