%0 Thesis %A He, Taotao %D 2019 %T New relaxations for composite functions %U https://hammer.purdue.edu/articles/thesis/New_relaxations_for_composite_functions/9118661 %R 10.25394/PGS.9118661.v1 %2 https://hammer.purdue.edu/ndownloader/files/16629167 %K MINLP %K Factorable Programming %K Convexification %K Composite Functions %K RLT %K MIP Relaxations %K Optimisation %X Mixed-integer nonlinear programs are typically solved using branch-and-bound algorithms. A key determinant of the success of such methods is their ability to construct tight and tractable relaxations. The predominant relaxation strategy used by most state-of-the-art solvers is the factorable programming technique. This technique recursively traverses the expression tree for each nonlinear function and relaxes each operator over a bounding box that covers the ranges for all the operands. While it is versatile, and allows finer control over the number of introduced variables, the factorable programming technique often leads to weak relaxations because it ignores operand structure while constructing the relaxation for the operator.