This talk will present HiGHS, a growing open-source repository of high-performance software for linear optimization based on award-winning computational techniques for the dual simplex method. The talk will give an insight into the work which has led to the creation of HiGHS and then set out the features which allows it to be used in a wide range of applications. Plans to extend the class of problems which can be solved using HiGHS will be set out.
Linear programming problems (LP) are widely solved in practice and reducing the solution time is essential for many applications. This talk will explore solving a sequence of unconstrained quadratic programming (QP) problems to derive an approximate solution and bound on the optimal objective value of an LP. Techniques for solving these QP problems fast will be discussed.
joint work with Ambros Gleixner, Thorsten Koch
We consider LPs of block diagonal structure with linking variables and constraints, motivated by energy system applications. To solve these problems, we have extended the interior-point solver PIPS-IPM (for stochastic QPs). This talk focuses on methods to handle large numbers of linking variables and constraints. A preconditioned iterative approach and a hierarchical algorithm will be presented, both of which exploit structure within the linking part. The extensions allow us to solve real-world problems with over 500 million variables and constraints in a few minutes on a supercomputer.