A Second Order Bundle Algorithm for Nonsmooth, Nonconvex Optimization Problems

Hermann Schichl () and Hannes Fendl ()
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Hermann Schichl: Faculty of Mathematics, University of Vienna
Hannes Fendl: Faculty of Mathematics, University of Vienna

Chapter Chapter 4 in Numerical Nonsmooth Optimization, 2020, pp 117-165 from Springer

Abstract: Abstract In this chapter we extend the SQP-approach of the well-known bundle-Newton method for nonsmooth unconstrained minimization and the second order bundle method by Fendl and Schichl (A feasible second order bundle algorithm for nonsmooth, nonconvex optimization problems with inequality constraints: I. derivation and convergence. arXiv:1506.07937, 2015, preprint) to the general nonlinearly constrained case. Instead of using a penalty function or a filter or an improvement function to deal with the presence of constraints, the search direction is determined by solving a convex quadratically constrained quadratic program to obtain good iteration points. Furthermore, global convergence of the method is shown under certain mild assumptions.

Date: 2020
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Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-3-030-34910-3_4

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DOI: 10.1007/978-3-030-34910-3_4

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