Journal
JOURNAL OF OPTIMIZATION THEORY AND APPLICATIONS
Volume 145, Issue 1, Pages 120-147Publisher
SPRINGER/PLENUM PUBLISHERS
DOI: 10.1007/s10957-009-9626-0
Keywords
Approximate optimization; Linear interpolation; Simplices; EPA Complex Emissions Model
Funding
- National Science Foundation [CBET-0827907]
- Div Of Chem, Bioeng, Env, & Transp Sys
- Directorate For Engineering [0827907] Funding Source: National Science Foundation
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We develop explicit, piecewise-linear formulations of functions f(x):ae (n) a dagger broken vertical bar ae, na parts per thousand currency sign3, that are defined on an orthogonal grid of vertex points. If mixed-integer linear optimization problems (MILPs) involving multidimensional piecewise-linear functions can be easily and efficiently solved to global optimality, then non-analytic functions can be used as an objective or constraint function for large optimization problems. Linear interpolation between fixed gridpoints can also be used to approximate generic, nonlinear functions, allowing us to approximately solve problems using mixed-integer linear optimization methods. Toward this end, we develop two different explicit formulations of piecewise-linear functions and discuss the consequences of integrating the formulations into an optimization problem.
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