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Erschienen in:
2019 | OriginalPaper | Buchkapitel
Efficient Piecewise Linearization for a Class of Non-convex Optimization Problems: Comparative Results and Extensions
verfasst von : Giorgio Fasano, János D. Pintér
Erschienen in: Modeling and Optimization: Theory and Applications
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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.