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© 2020

Numerical Nonsmooth Optimization

State of the Art Algorithms

  • Adil M. Bagirov
  • Manlio Gaudioso
  • Napsu Karmitsa
  • Marko M. Mäkelä
  • Sona Taheri
Book

Table of contents

  1. Front Matter
    Pages i-xvii
  2. Adil M. Bagirov, Manlio Gaudioso, Napsu Karmitsa, Marko M. Mäkelä, Sona Taheri
    Pages 1-16
  3. General Methods

    1. Front Matter
      Pages 17-17
    2. Pavel E. Dvurechensky, Alexander V. Gasnikov, Evgeni A. Nurminski, Fedor S. Stonyakin
      Pages 19-59
    3. James V. Burke, Frank E. Curtis, Adrian S. Lewis, Michael L. Overton, Lucas E. A. Simões
      Pages 201-225
  4. Structure Exploiting Methods

    1. Front Matter
      Pages 227-227
    2. Kaisa Joki, Adil M. Bagirov
      Pages 263-296
    3. Shuai Liu, Claudia Sagastizábal
      Pages 297-329
    4. Andreas Griewank, Andrea Walther
      Pages 331-361
    5. Ladislav Lukšan, Ctirad Matonoha, Jan Vlček
      Pages 363-414
  5. Methods for Special Problems

    1. Front Matter
      Pages 415-415
    2. Welington de Oliveira, Mikhail Solodov
      Pages 417-459
    3. Outi Montonen, Kaisa Joki
      Pages 481-497
    4. Ann-Brith Strömberg, Torbjörn Larsson, Michael Patriksson
      Pages 499-547
    5. Ville-Pekka Eronen, Tapio Westerlund, Marko M. Mäkelä
      Pages 549-578

About this book

Introduction

Solving nonsmooth optimization (NSO) problems is critical in many practical applications and real-world modeling systems. The aim of this book is to survey various numerical methods for solving NSO problems and to provide an overview of the latest developments in the field. Experts from around the world share their perspectives on specific aspects of numerical NSO. 

The book is divided into four parts, the first of which considers general methods including subgradient, bundle and gradient sampling methods. In turn, the second focuses on methods that exploit the problem’s special structure, e.g. algorithms for nonsmooth DC programming, VU decomposition techniques, and algorithms for minimax and piecewise differentiable problems. The third part considers methods for special problems like multiobjective and mixed integer NSO, and problems involving inexact data, while the last part highlights the latest advancements in derivative-free NSO. 

Given its scope, the book is ideal for students attending courses on numerical nonsmooth optimization, for lecturers who teach optimization courses, and for practitioners who apply nonsmooth optimization methods in engineering, artificial intelligence, machine learning, and business. Furthermore, it can serve as a reference text for experts dealing with nonsmooth optimization.

Keywords

Bundle methods Nondifferentiable optimization Nonsmooth analysis Subgradient methods Test problems Piecewise smooth Stochastic methods for NSO Inexact data Noncontinuous NSO NSO Discrete gradient based methods Penalty functions Linearization Derivative free methods

Editors and affiliations

  • Adil M. Bagirov
    • 1
  • Manlio Gaudioso
    • 2
  • Napsu Karmitsa
    • 3
  • Marko M. Mäkelä
    • 4
  • Sona Taheri
    • 5
  1. 1.School of Science, Engineering and Information TechnologyFederation University AustraliaBallaratAustralia
  2. 2.Department of Informatics, Modeling, Electronics and System EngineeringUniversity of CalabriaRende (CS)Italy
  3. 3.Department of Mathematics and StatisticsUniversity of TurkuTurkuFinland
  4. 4.Department of Mathematics and StatisticsUniversity of TurkuTurkuFinland
  5. 5.School of Science, Engineering and Information TechnologyFederation University AustraliaBallaratAustralia

About the editors

Adil M. Bagirov received a master degree in Applied Mathematics from Baku State University, Azerbaijan in 1983, and the Candidate of Sciences degree in Mathematical Cybernetics from the Institute of Cybernetics of Azerbaijan National Academy of Sciences in 1989 and PhD degree in Optimization from Federation University Australia (formerly the University of Ballarat), Ballarat, Australia in 2002. He worked at the Space Research Institute (Baku, Azerbaijan), Baku State University (Baku, Azerbaijan), Joint Institute for Nuclear Research (Moscow, Russia). Dr. Bagirov is with Federation University Australia (Ballarat, Australia) since 1999. He currently holds the Associate Professor position at this university. He has won five Australian Research Council Discovery and Linkage grants to conduct research in nonsmooth and global optimization and their applications. He was awarded Australian Research Council Postdoctoral Fellow and Australian Research Council Research Fellow. His main research interests are in the area of nonsmooth and global optimization and their applications in data mining, regression analysis and water management. Dr. Bagirov has published two books on nonsmooth optimization and its applications and more than 150 journal papers, book chapters and papers in conference proceedings.

Manlio Gaudioso got his  “Laurea” degree in Electrical Engineering from Università di Napoli in 1973. Since 1994 he is full professor  of Operations Research at Università della Calabria. His research interests include nonsmooth optimization, integer programming, graph optimization, logistic chain optimization and classification methods in machine learning. He is currently Associate Editor of the journal “Optimization” and of “Vestnik of Saint Petersburg University”.  He plays drums in the Italian Jazz Band “Ars Brevis”.

Napsu Karmitsa (nee Haarala) received her Ph.D. degree from the University of Jyväskylä, Finland, in 2004. At the moment, she holds a position of the Academy Research Fellow granted by the Academy of Finland. In addition, she is an Adjunct Professor in applied mathematics at the University of Turku, Finland. Karmitsa’s research is focused on nonsmooth optimization and analysis. Special emphasis is given to nonconvex, global and large-scale cases, and applications in data mining and machine learning. Her previous book "Introduction to Nonsmooth Optimization: Theory, Practice and Software" (Springer 2014), coauthored with Profs. Adil Bagirov and Marko M. Mäkelä, is the first easy-to-read book on nonsmooth optimization and it is currently a widely used textbook in the area of nonsmooth analysis and optimization. In addition, her forthcoming book "Partitional Clustering via Nonsmooth Optimization: Cluster Analysis via Optimization" (Springer, 2019) coauthored with Prof. Adil Bagirov and PhD. Sona Taheri considers applying nonsmooth optimization in an important practical field of data mining.

Marko M. Mäkelä currently holds the full professorship in Applied Mathematics at the University Turku, Finland. He is also a vice head of the Department of Mathematics and Statistics at the University of Turku. He obtained his MSc degree in Applied Mathematics in 1986 and PhD degree in Scientific Computing in 1990 both from the University of Jyväskylä, Finland. He still holds a Adjunct Professor position at the University of Jyväskylä. Prof. Mäkeläs’ research is focused mainly on nonsmooth analysis and optimization. Special emphasis has been on nonsmooth and nonconvex analysis including optimality conditions and the theory of generalized convexities, together with designing numerical methods for nonsmooth nonconvex optimization. In addition, his research interests include mixed-integer nonlinear programming, multiobjective optimization, metaheuristics in global optimization and industrial applications. He has published two textbooks on nonsmooth optimization and more than one hundred scientific articles. He is currently a Handling Editor of the Journal of Nonsmooth Analysis and Optimization. He plays the clarinet in a wind orchestra and in a dixieband.

Sona Taheri is a Research Fellow at Federation University Australia. Dr Taheri has been at this University since 2009. She has received her PhD degree in Mathematics at this university (formerly the University of Ballarat) in 2012. Underpinning this is her Master degree in Applied Mathematics and Bachelor of Science in Pure Mathematics through University of Tabriz Iran completed in 2004 and 2001, respectively. Dr Taheri’s main research interests include nonconvex and nonsmooth optimization, and their applications in data mining. She is one of the authors (together with Profs. Adil Bagirov and Napsu Karmitsa) of the forthcoming book "Partitional Clustering via Nonsmooth Optimization:Cluster Analysis via Optimization" (Springer, 2019).

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