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Efficient Piecewise Linearization for a Class of Non-convex Optimization Problems: Comparative Results and Extensions

  • Giorgio FasanoEmail author
  • János D. Pintér
Conference paper
Part of the Springer Proceedings in Mathematics & Statistics book series (PROMS, volume 279)

Abstract

This research work originates from a challenging control problem in space engineering that gives rise to hard nonlinear optimization issues. Specifically, we need the piecewise linearization (PL) of a large number of non-convex univariate functions, within a mixed integer linear programming (MILP) framework. For comparative purposes, we recall a well-known classical PL formulation, an alternative approach based on disaggregated convex combination (DCC), and a more recent approach proposed by Vielma and Nemhauser. Our analysis indicates that—in the specific context of our study—the DCC-based approach has computational advantages: this finding is supported by experimental results. We discuss extensions and variations of the basic DCC paradigm. Extensions to a number of possible application areas in robotics and automation are also envisioned.

Keywords

Separable functions Piecewise linearization of non-convex univariate and multivariate functions Large-scale mixed integer linear programming Nonlinear programming Global optimization Comparative numerical experiments Control problems Control dispatch optimization Space engineering and other applications 

MSC Classification (2010)

90C06 90C11 90C26 90C30 90C59 90C90 

Notes

Acknowledgements

The authors thank Laureano Escudero for his interest and comments related to the present work.

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Copyright information

© Springer Nature Switzerland AG 2019

Authors and Affiliations

  1. 1.Thales Alenia SpaceTurinItaly
  2. 2.Lehigh UniversityBethlehemUSA

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