Sentence examples for bound for the optimal from inspiring English sources

We formulate this problem as an integer-programming problem and present a Lagrangian relaxation method which, for each choice of Lagrangian multipliers, provides a lower bound for the optimal objective function value.

On the same basis, of course, America's rate is far too low (even a lower bound for the optimal rate would be a lot higher than 7 pence a litre).Britain's rate, judged according to the environmental and congestion arguments, looks way too high but plainly the British government has another reason for taxing petrol so heavily.

This point is a lower bound for the optimal solution.

The corresponding optimal value of the dual problem D ∗ is the lower bound for the optimal value of the approximated primal problem in (12), denoted as P ∗, given by P^geq D^. (22).

Then, the relative gap for this solution measures the distance between z B and the available best bound for the optimal objective function value (z L ) using the ratio | z B − z L | z L. LP-based branch-and-bound algorithms are used for solving MIPs in GAMS [31]; thus, z L is the LP relaxation solution of the MIP problem under consideration.

When a constraint in a maximization problem is modified (perturbed) in such a way that it gets tightened, the optimal value of the perturbed problem is always a lower bound for the optimal value of the original problem (see pp. 249-251 in [31]).

Next, we prove that the bound for the sum is optimal in each case.

(1) for ; (2) for, and for, moreover, in each case, the bound for the sum is optimal.

Based on a lower bound for the weight of the optimal schedule (that can be obtained, for example, by running the greedy algorithm), the search tree can also be conservatively pruned using the following heuristic: a subtree is pruned if weight of partial schedule + weight of instances to schedule

This method has a quadratic cost in the number of particles but provides the optimal bound for the algorithm of Lemma 1.

In Figure 2 we show that the optimal bound for the strain sensitivity provided by the QFI is very robust to initial temperatures.