Efficient Piecewise Linearization for a Class of Non-convex Optimization Problems: Comparative Results and Extensions
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.
KeywordsSeparable 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
The authors thank Laureano Escudero for his interest and comments related to the present work.
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