Piecewise-Linear Approximations of Multidimensional Functions |
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Authors: | R Misener C A Floudas |
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Institution: | (3) Tokyo Inst. Technol., Tokyo, Japan |
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Abstract: | We develop explicit, piecewise-linear formulations of functions f(x):ℝ
n
↦ℝ, n≤3, 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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Keywords: | |
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