In this chapter we review some deterministic solution methods for convex mixed integer nonsmooth optimization problems. The methods are branch and bound, outer approximation, extended cutting plane, extended supporting hyperplane and extended level bundle method. Nonsmoothness is taken into account by using Clarke subgradients as a substitute for the classical gradient. Ideas for convergence proofs are given as well as references where the details can be found. We also consider how some algorithms can be modified in order to solve nonconvex problems including f∘-pseudoconvex functions or even f∘-quasiconvex constraints.
|Title of host publication||Numerical Nonsmooth Optimization|
|Subtitle of host publication||State of the Art Algorithms|
|Editors||Adil M. Bagirov, Manlio Gaudioso, Napsu Karmitsa, Marko M. Mäkelä, Sona Taheri|
|Number of pages||30|
|Publication status||Published - 2020|
|MoE publication type||A3 Part of a book or another research book|