Tuesday, 16:15 - 16:40 h, Room: H 2053


Angelos Tsoukalas
Extension of McCormick's composition to multi-variate outer functions

Coauthor: Alexander Mitsos


G. P. McCormick [Math Prog 1976] provides the framework for the convex/concave relaxations of factorable functions involving functions of the form Fº f, where F is a univariate function. We give a natural reformulation of McCormick's Composition theorem which allows for a straight forward extension to multi-variate outer functions. In addition to extending the framework, we show how the result can be used in the construction of relaxation proofs.
A direct consequence is an improved relaxation for the product of two functions which is at least as tight and some times tighter than McCormick's result. We also apply the composition result to the minimum/maximum and the division of two functions yielding an improvement on the current relaxation. Finally we interpret McCormick's Composition theorem as a decomposition approach to the auxiliary variable reformulation methods and we introduce some ideas for future hybrid variations.


Talk 3 of the invited session Tue.3.H 2053
"From quadratic through factorable to black-box global optimization" [...]
Cluster 9
"Global optimization" [...]


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