It is well-known that solutions to parametric linear or quadratic programs are continuous piecewise affine functions of the parameter. In this paper we prove the converse, i.e. that every continuous ...

We study the modeling of nonconvex piecewise-linear functions as mixed-integer programming (MIP) problems. We review several new and existing MIP formulations for continuous piecewise-linear functions ...

We define two functions f and g on the unit interval [0, 1] to be strongly conjugate $\operatorname {iff}$ there is an order-preserving homeomorphism h of [0, 1] such that g = h -1 fh (a minor ...