Certifying and repairing solutions to large LPs how good are LP-solvers?
SODA '03 Proceedings of the fourteenth annual ACM-SIAM symposium on Discrete algorithms
Rigorous Lower and Upper Bounds in Linear Programming
SIAM Journal on Optimization
Safe bounds in linear and mixed-integer linear programming
Mathematical Programming: Series A and B
The Traveling Salesman Problem: A Computational Study (Princeton Series in Applied Mathematics)
The Traveling Salesman Problem: A Computational Study (Princeton Series in Applied Mathematics)
Fast and Accurate Bounds on Linear Programs
SEA '09 Proceedings of the 8th International Symposium on Experimental Algorithms
An exact rational mixed-integer programming solver
IPCO'11 Proceedings of the 15th international conference on Integer programming and combinatoral optimization
Operations Research Letters
Exact solutions to linear programming problems
Operations Research Letters
Operations Research Letters
Computers and Operations Research
| Hi-index | 0.00 |
Fast computation of valid linear programming LP bounds serves as an important subroutine for solving mixed-integer programming problems exactly. We introduce a new method for computing valid LP bounds designed for this application. The algorithm corrects approximate LP dual solutions to be exactly feasible, giving a valid bound. Solutions are repaired by performing a projection and a shift to ensure all constraints are satisfied; bound computations are accelerated by reusing structural information through the branch-and-bound tree. We demonstrate this method to be widely applicable and faster than solving a sequence of exact LPs. Several variations of the algorithm are described and computationally evaluated in an exact branch-and-bound algorithm within the mixed-integer programming framework SCIP Solving Constraint Integer Programming.