Generating Optimal Robust Continuous Piecewise Linear Regression with Outliers Through Combinatorial Benders Decomposition

Using piecewise linear (PWL) functions to model discrete data has applications for example in healthcare, engineering and pattern recognition. Recently, mixed-integer linear programming (MILP) approaches have been used to optimally fit continuous PWL functions. We extend these formulations to allow for outliers. The resulting MILP models rely on binary variables and big-M constructs to model … Read more

Stochastic Dual Dynamic Programming And Its Variants

We provide a tutorial-type review on stochastic dual dynamic programming (SDDP), as one of the state-of-the-art solution methods for multistage stochastic programs. Since introduced about 30 years ago for solving large-scale multistage stochastic linear programming problems in a hydrothermal context, SDDP has been applied to practical problems from several fields and is enriched by various … Read more

A Comparison of two Mixed-Integer Linear Programs for Piecewise Linear Function Fitting

The problem of fitting continuous piecewise linear (PWL) functions to discrete data has applications in pattern recognition and engineering, amongst many others. To find an optimal PWL function, it is required that the positioning of the breakpoints connecting adjacent linear segments are not constrained, and are allowed to be placed freely. While the PWL fitting … Read more