An Algorithm for Linearly Constrained Piecewise Lexicographic Programming Problems

The Linear Piecewise Lexicographic Programming (LPWLGP) problem is a mathematical programming model with linear constraints and several piecewise linear objective functions, arranged in a lexicographic hierarchy. Lexicographic spaces are introduced, and the differential properties of functions taking values in them are discussed. Necessary and sufficient optimality conditions for the LPWLGP problem are derived, and an algorithm based on them is formulated