Sentence examples for bound to the optimal from inspiring English sources

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.

Obviously this will give us a lower bound to the optimal primal solution.

Because the dual solution is not necessarily primal feasible, we also present an algorithm to get a feasible point from the dual solution, which is a lower bound to the optimal primal solution.

The following lemma delineates the correctness of the obtained upper bound to the optimal score in the pre-processing step.

So, the score of any size- k' subgraph is actually an upper bound to the optimal score value.

However, there can be no such e i as the pre-processing step selects k edges with the smallest ϕ values in the template graph, T. Therefore, the lower bound obtained in the pre-processing step is indeed a lower bound to the score of optimal subgraph.

The score of a size-k subgraph computed as in the above pre-processing step is a lower bound to the score of an optimal size-k subgraph.

Assume that the score(G) is not a lower bound to the score of an optimal size- k subgraph (i.e., score(G) > score(G*)).

This approach could effectively bridge the gap until the causative microbes have been identified (for example, by blood culture or by analyzing the pathogens bound to the magnetic beads) and optimal antibiotic therapy can be initiated.

The variational parameters from the inference step provide the optimal lower bound to the log-likelihood of (x i,y i ), and maximizing the aggregate lower bound (sum _{i=1}^{mathcal {M}}mathcal {L}(gamma ^,phi ^,xi ^,alpha,Omega,eta)) over all data points with respect to α, Ω and η, respectively, yields the estimated parameters.

However, Rfx3 (Rfx3 expression is unaffected in Rfx6ΔBeta islets) was not sufficient to compensate for the absence of Rfx6, regarding Gck expression, suggesting that Rfx3-Rfx6 heterodimers bind to the Gck promoter for the optimal transcription of Gck gene.