Séminaire 'Un chercheur du GERAD vous parle!'

Titre :  Towards the biconjugate of bivariate piecewise quadratic functions

Conférencier : Yves Lucet – Université de la Colombie-Britannique, Canada

Computing the closed convex envelope or biconjugate is the core operation that bridges the domain of nonconvex with convex analysis. We focus here on computing the conjugate of a bivariate piecewise quadratic function defined over a polytope. First, we compute the convex envelope of each piece, which is characterized by a polyhedral subdivision such that over each member of the subdivision, it has a rational form (square of a linear function over a linear function). Then we compute the conjugate of all such rational functions. It is observed that the conjugate has a parabolic subdivision such that over each member of its subdivision, it has a fractional form (linear function over square root of a linear function). This computation of the conjugate is performed with a worst-case linear time complexity algorithm.

Our results are an important step toward computing the conjugate of a piecewise quadratic function, and further in obtaining explicit formulas for the convex envelope of piecewise rational functions.

This is joint work with MSc D. Kumar.

---

Entrée gratuite.
Bienvenue à tous!