10h30 - 12h00
Modeling and optimization using IPsolve
IPsolve is an interior point method that exploits conjugate representations of PLQ penalties. In this tutorial, we will begin with a set of penalties used in machine learning and signal processing, and work with their convex conjugates to get a uniform representation used by IPsolve for modeling. PLQ penalties include least square (regression, kernel machines), huber (robust regression), 1-norm (sparse regularization), asymmetric 1-norm (quantile regression), hinge loss (support vector machines), and many others, including CVAR for financial applications. We will go through several application examples, in each case modeling and solving them using IPsolve. The tutorial will focus on modeling in different application domains, with some supporting material from convex analysis to go between problem representations.