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An Interior-Point Method for Nonlinear Optimization Problems with Locatable and Separable Nonsmoothness

Martin Schmidt (mar.schmidt***at***fau.de)

Abstract: A lot of real-world optimization models comprise nonconvex and nonlinear as well as nonsmooth functions leading to very hard classes of optimization models. In this article a new interior-point method for the special but practically relevant class of optimization problems with locatable and separable nonsmooth aspects is presented. After motivating and formalizing the problems under consideration, modifications and extensions to standard interior-point methods for nonlinear programming are investigated in order to solve the introduced problem class. First theoretical results are given and a numerical study is presented that shows the applicability of the new method for real-world instances from gas network optimization.

Keywords: Interior-point methods, Barrier methods, Line-search methods, Nonlinear and nonsmooth optimization, Classification of optimization models, Gas network optimization

Category 1: Nonlinear Optimization (Constrained Nonlinear Optimization )

Category 2: Convex and Nonsmooth Optimization (Nonsmooth Optimization )

Category 3: Applications -- Science and Engineering

Citation: Technical report, (a) Friedrich-Alexander-Universität Erlangen-Nürnberg (FAU), Department Mathematik, Lehrstuhl für Wirtschaftsmathematik, Cauerstraße 11, 91058 Erlangen, Germany; (b) Energie Campus Nürnberg, Fürther Straße 250, 90429 Nürnberg, Germany. April 2014

Download: [PDF]

Entry Submitted: 04/29/2014
Entry Accepted: 04/29/2014
Entry Last Modified: 10/23/2014

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