53 citations · 292 across the 29 of their papers we have counts for
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A mixed-integer branching approach for very small formulations of disjunctive constraints
Joey Huchette, Juan Pablo Vielma
An important problem in optimization is the construction of mixed-integer programming (MIP) formulations of disjunctive constraints that are both strong and small. Motivated by low…
Nonconvex piecewise linear functions: Advanced formulations and simple modeling tools
Joey Huchette, Juan Pablo Vielma
We present novel mixed-integer programming (MIP) formulations for optimization over nonconvex piecewise linear functions. We exploit recent advances in the systematic construction…
Mixed-integer convex representability
Miles Lubin, Juan Pablo Vielma, Ilias Zadik
Motivated by recent advances in solution methods for mixed-integer convex optimization (MICP), we study the fundamental and open question of which sets can be represented exactly a…
Small and Strong Formulations for Unions of Convex Sets from the Cayley Embedding
Juan Pablo Vielma
There is often a significant trade-off between formulation strength and size in mixed integer programming (MIP). When modeling convex disjunctive constraints (e.g. unions of convex…