Sentence examples for valid lower bound from inspiring English sources

The subproblems are first approximated by an adaptive piece-wise linearization scheme that provides lower bounds, and the MILP is further relaxed to an LP to improve solution efficiency while providing a valid lower bound.

We show by a counterexample that the dual-ascent procedure proposed by Herrmann, Ioannou, Minis and Proth in a 1996 issue of the European Journal of Operational Research is incorrect in the sense that it does not generate a valid lower bound to the optimal value of fixed-charge capacitated network design problems.

The tight lower bound presented here is a valid lower bound if the point-to-point codes are first decoded, followed by the network code, without iterating back to the point-to-point codes.

Then the procedure (R a) must produce a valid lower bound.

Note that the heuristic approximation of R u is still a valid upper bound, but that of any lower bound may not be a valid lower bound.

Bafna and Bansal [ 11] has proved that R I is a valid lower bound of R min given a particular order of the sequences.

We develop valid inequalities that enhance the lower bound and propose a local search heuristic procedure that improves the upper bound.

The lower bound is valid for any C-benevolent instance, some D-benevolent functions and for unit intervals.

Finally, we prove that the given lower bound remains valid for the 3-dimensional case as well.

This lower bound is valid for every cutting method.

- Deterministic communication complexity lower bounds techniques: Tiling lower bound (section 12.2.2), Fooling sets (section 12.2.1), the rank lower bound and the log-rank conjecture (section 12.2.3).