On Mixed Integer Nonsmooth Optimization

Ville-Pekka Eronen (), Tapio Westerlund () and Marko M. Mäkelä ()
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Ville-Pekka Eronen: University of Turku, Department of Mathematics and Statistics
Tapio Westerlund: University of Turku, Department of Mathematics and Statistics
Marko M. Mäkelä: University of Turku, Department of Mathematics and Statistics

Chapter Chapter 16 in Numerical Nonsmooth Optimization, 2020, pp 549-578 from Springer

Abstract: Abstract 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.

Date: 2020
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Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-3-030-34910-3_16

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DOI: 10.1007/978-3-030-34910-3_16

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