Zoom link: https://upenn.zoom.us/j/98220304722

A Heaviside function is an indicator function of a semi-infinite interval. A Heaviside composite function is a Heaviside function composed with a multivariate function that may be nonsnooth. This talk presents a touch of this novel class of discontinuous optimization problems that borders on continuous and discrete optimization. Among the rich applications of such problems, we mention one pertaining to classification and treatment with constraints solvable by an elementary yet novel progressive integer programming (PIP) method that can be applied broadly to many other problems,​ including indefinite quadratic programs and linear programs with linear​ complementarity constraints.  Computational results demonstrate the excellent​ performance of the PIP idea and its superiority over a full integer programming approach.