Numerical nonsmooth optimization

Aim of the book

The aim of the forthcoming book is to survey different kind of numerical methods developed for nonsmooth optimization (NSO) and to give an overview to the most resent developments in the area. The book will cover both traditional methods and the methods developed for problems with special structures. The surveys will be written by the top authors on the field.

Nonsmooth optimization (NSO) refers to the general problem of minimizing (or maximizing) functions that are typically not differentiable at their minimizers (maximizers). These kinds of functions can be found in many applied fields, for example in image denoising, optimal control, neural network training, data mining, economics, and computational chemistry and physics. Since classical theory of optimization presumes certain differentiability and strong regularity assumptions for the functions to be optimized, it cannot be directly utilized, nor can the methods developed for smooth problems.

The book is aimed for post graduate students, professionals, and practitioners who know classical optimization, and the fact that it is not always enough. It will be published by Springer in 2019.

List of contents and contributors

General methods

• Advances in low-memory subgradient optimization, P.E. Dvurechensky, A.V. Gasnikov, E.A. Nurminski, and F.S. Stonyakin
• Standard bundle methods: untrusted models and duality, A. Frangioni
• Gradient sampling methods for nonsmooth optimization, J.V. Burke, F.E. Curtis, A.S. Lewis, M.L. Overton, and L.E.A. Simoes
• A second order bundle algorithm for nonsmooth, nonconvex optimization problems, H. Schichl and H. Fendl
• Limited memory bundle method and its variations for large-scale nonsmooth optimization, N. Karmitsa

Structure exploiting methods

• Local search for nonsmooth DC optimization with DC equality and inequality constraints, A. Strekalovsky
• Bundle methods for nonsmooth DC optimization, K. Joki and A. Bagirov
• Beyond first order: VU-decomposition methods, S. Liu and C. Sagastizabal
• Beyond the oracle: opportunities of piecewise differentiation, A. Griewank and A. Walther
• Numerical solution of generalized minimax problems, L. Luksan, C. Matonoha, and J. Vlcek

Methods for special problems

• Scaled improvement functions in nonsmooth multiobjective optimization, M. Mäkelä and O. Montonen
• Multiobjective double bundle method for DC optimization, O. Montonen and K. Joki
• Dual subgradient methods for integer problems, M. Patriksson, A.-B. Strömberg, and T. Larsson
• Lagrangian relaxations of integer problems, M. Gaudioso
• On mixed integer nonsmooth optimization, V.-P. Eronen, T. Westerlund, and M.M. Mäkelä
• Bundle methods for inexact data, W. de Oliveira and M. Solodov

Derivative free methods

• Discrete gradient method and LDGB, A. Bagirov, S. Taheri, and N. Karmitsa
• Model-based methods in derivative-free nonsmooth optimization, C. Audet and W. Hare