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1017. On the Piecewise Convex Approximations of Two-Variables Functions
Invited abstract in session TB-4: Topics in Mixed Integer Nonlinear Programming 1, stream MINLP.
Tuesday, 10:30-12:00Room: 1001 (building: 202)
Authors (first author is the speaker)
| 1. | Claudia D'Ambrosio
|
| LIX, CNRS - Ecole Polytechnique | |
| 2. | Antonio Frangioni
|
| Dipartimento di Informatica, Universita' di Pisa | |
| 3. | Claudio Gentile
|
| IASI-CNR |
Abstract
In the literature, different approaches have been proposed to approximate two-variable nonlinear functions. In particular, classic piecewise linear approximation, based on triangulation of the function domain is one of the most widely used in practice.
We start from a different approach, originally proposed in Rovatti et al. (2014), that allows one to obtain piecewise linear approximation by dividing into rectangles the nonlinear function domain. Rovatti et al. studied formulations for modeling such an approximation, using a number of binary variables that is equal to j + k, where j (respectively, k) is the number of intervals in which the first (resp. second) variable is divided. Note that the classic formulations of piecewise linear approximations based on triangulations need 2 x j x k binary variables instead.
In this work, we consider the generalization of the work by Rovatti et al. (2014) to the piecewise convex approximation case. In particular, we explore the strengthening of mathematical formulations to model such approximations via perspective reformulations. Finally, we show their interest thanks to some preliminary computational results.
Keywords
- Programming, Mixed-Integer
- Convex Optimization
- Combinatorial Optimization
Status: accepted
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