Benoît Legat

Polyhedra are at the foundation of many engineering tools such as Mixed-Integer Programming. Manipulating them can give key insights

Polyhedra are at the foundation of many engineering tools such as Mixed-Integer Programming and Computational Geometry. Manipulating them can give key insights but the operations on polyhedra, commonly referred to as Polyhedral Computation can be very costly.
This talk introduces an interface for Polyhedral Computation that is implemented by the main libraries that exist nowadays as well the implementation of these algorithms in Julia.

AdaptiveHierarchicalRegularBinning

32-124

Polyhedral Computation

Polynomial Optimization can be solved in a variety of ways. JuMP provides an unified interface for modelling these problems. In this talk, we show how to interface each type of polynomial optimization solver to this model and how they compare on a variety of benchmark problems.

Polynomial Optimization can be solved in a variety of ways. Black-box solvers using first and second-order derivative callbacks can be used but these only find a local extremum and cannot guarantee its global optimality. Several approaches exist to find the global optimum. These include Sum-of-Squares, Sums of AM/GM Exponential, multivariate partitioning algorithm and Algebraic System solving of the KKT conditions. In this talk, we detail the work of bringing all these possible solving strategies to the common JuMP nonlinear interface. We then compare the efficiency of these approaches both in theory and in practice on a variety of benchmark problems.

Benoît Legat

Talks:

Polyhedral Computation

Polynomial Optimization

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