Invited Session Mon.2.MA 004

Monday, 13:15 - 14:45 h, Room: MA 004

Cluster 11: Integer & mixed-integer programming [...]

New methodologies for mixed-integer programming


Chair: Daniel Bienstock



Monday, 13:15 - 13:40 h, Room: MA 004, Talk 1

Juan Pablo Vielma
Split cuts for convex nonlinear mixed integer programming

Coauthors: Daniel Dadush, Santanu Dey, Mustafa Kilinc, Sina Modaresi


In this talk we study split cuts for convex nonlinear mixed integer programming. We give closed form expressions of split cuts for some quadratic sets and show that the split closure of a strictly convex set is generated by a finite number of split disjunctions, but is not necessarily a polyhedron.



Monday, 13:45 - 14:10 h, Room: MA 004, Talk 2

Daniel Bienstock
Strong formulations for convex functions over nonconvex sets

Coauthor: Alexander Michalka


In this paper we derive strong linear inequalities for systems representing a convex quadratic over the complement of a convex set, and we present, in several cases, characterizations of the convex hull by polynomially separable linear inequalities. An example of this situation is that of positive definite quadratic over the complement of a polyhedron.



Monday, 14:15 - 14:40 h, Room: MA 004, Talk 3

Diego Moran
Strong dual for conic mixed-integer programs

Coauthors: Santanu Subhas Dey, Juan Pablo Vielma


Mixed-integer conic programming is a generalization of mixed-integer linear programming. We present an extension of the duality theory for mixed-integer linear programming to the case of mixed-integer conic programming. Under a simple condition on the primal problem, we are able to prove strong duality.


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