Inductive Linearization for Binary Quadratic Programs with Linear Constraints: A Computational Study

The computational performance of inductive linearizations for binary quadratic programs in combination with a mixed-integer programming solver is investigated for several combinatorial optimization problems and established benchmark instances. Apparently, a few of these are solved to optimality for the first time. Citation preprint (no internal series / number): University of Bonn, Germany June 11, 2021 … Read more

A fully mixed-integer linear programming formulation for economic dispatch with valve-point effects, transmission loss and prohibited operating zones

Economic dispatch (ED) problem considering valve-point effects (VPE), transmission loss and prohibited operating zones (POZ) is a very challenging issue due to its intrinsic non-convex, non-smooth and non-continuous natures. To achieve a near globally solution, a fully mixed-integer linear programming (FMILP) formulation is proposed for such an ED problem. Since the original loss function is … Read more

Solution for short-term hydrothermal scheduling with a logarithmic size MILP formulation

Short-term hydrothermal scheduling (STHS) is a non-convex and non-differentiable optimization problem that is difficult to solve efficiently. One of the most popular strategy is to reformulate the complicated STHS by various linearization techniques that makes the problem easy to solve. However, in this process, a large number of extra continuous variables, binary variables and constraints … Read more

Optimization by the Fixed-Point Method, Version 2.17

Abstract: After developing necessary background theory, the original primal and dual are specified, and the invariant primal and dual LP’s are defined. Pairs of linear mappings are defined which establish an effectively one-to-one correspondences between solutions to the original and invariant problems. The invariant problems are recast as a fixed-point problem and precise solution conditions … Read more