An enumerative method for convex programs with linear complementarity constraints and application to the bilevel problem of a forecast model for high complexity products

Heß, Maximilian

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URN: urn:nbn:de:bsz:180-madoc-438553
Document Type: Doctoral dissertation
Year of publication: 2017
Place of publication: Mannheim
University: Universität Mannheim
Evaluator: Göttlich, Simone
Date of oral examination: 24 November 2017
Publication language: English
Institution: School of Business Informatics and Mathematics > Angewandte Mathematik (Juniorprofessur) (Kolb 2012-2021)
School of Business Informatics and Mathematics > Mathematische Optimierung (Schillings 2017-2022)
School of Business Informatics and Mathematics > Scientific Computing (Göttlich 2011-)
Subject: 510 Mathematics
Subject headings (SWD): Optimierung
Keywords (English): Optimization , MPEC , CASET , BBASET
Abstract: The increasing variety of high complexity products presents a challenge in acquiring detailed demand forecasts. Against this backdrop, a convex quadratic parameter dependent forecast model is revisited, which calculates a prognosis for structural parts based on historical order data. The parameter dependency inspires a bilevel problem with convex objective function, that allows for the calculation of optimal parameter settings in the forecast model. The bilevel problem can be formulated as a mathematical problem with equilibrium constraints (MPEC), which has a convex objective function and linear constraints. Several new enumerative methods are presented, that find stationary points or global optima for this problem class. An algorithmic concept shows a recursive pattern, which finds global optima of a convex objective function on a general non-convex set defined by a union of polytopes. Inspired by these concepts the thesis investigates two implementations for MPECs, a search algorithm and a hybrid algorithm.

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