Amitabh Basu

We consider the problem of minimizing a convex function under convex constraints, where some or all of the decision variables are constrained to be integer, with access to first-order oracles for the objective function and separation oracles for the...

Cutting plane techniques are key to solving large scale optimization problems with mixed-integer variables. Modern approaches to cutting plane theory shows that the concept of sublinearity is a unifying way to organize these ideas. This leads to a...

It is well-known that a closed convex set C containing the origin in its interior can be represented as the 1-sublevel set of its gauge function. If the set C is compact, then the gauge is the unique sublinear function whose 1-sublevel coincides with...