Friday, 16:15 - 16:40 h, Room: MA 041

 

Claudia D'Ambrosio
Optimistic modeling of non-linear optimization problems by mixed-integer linear programming

Coauthors: Andrea Lodi, Riccardo Rovatti, Martello Silvano

 

Abstract:
We present a new piecewise linear approximation of non-linear optimization problems. It can be seen as a variant of classical triangulations that leaves more degrees of freedom to define any point as a convex combination of the samples. For a hyper-rectangular domain URL, partitioned into hyper-rectangular subdomains through a grid defined by nl points on the l-axis (l=1, … ,L), the number of potential simplexes is L! \prodl=1L(nl-1), and an MILP model incorporating it without complicated encoding strategies must have the same number of additional binary variables. In the proposed approach the choice of the simplexes is optimistically guided by one between two approximating objective functions, and the number of additional binary variables needed by a straightforward implementation drops to only l=1L(nl-1). The method allows the use of recent methods for representing such a partition with a logarithmic number of constraints and binary variables.
We show theoretical properties of the approximating functions, and provide computational evidence of the impact of the method when embedded in MILP models.

 

Talk 3 of the invited session Fri.3.MA 041
"Modelling, reformulation and solution of MINLPs" [...]
Cluster 14
"Mixed-integer nonlinear programming" [...]

 

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