The phrase "as single level" is not correct in standard written English.
It may be intended to describe something that is at a single level or layer, but it lacks clarity and proper context.
Example: "The design of the building is as single level, which makes it easier to navigate."
Alternatives: "at a single level" or "on one level".
The proposed models are first formulated as multi-level programming problems and then recast, under certain assumptions, as single-level mixed-integer linear or non-linear optimization problems using duality theory.
These are all structured as single-level-controlled vocabularies with synonyms, described in (3).
In this section, the SOCBLP problem (1) in the optimistic case is reformulated as a single level optimization problem by using the Karush-Kuhn-Tucker (KKT) conditions for the lower level problem.
In this subsection, we reformulate problem (21) as a single level optimization problem, and then we discuss its optimization conditions under strict complementarity and linear independence constraint qualification assumptions.
Then some examples illustrate that the SOCBLP is generally a nonconvex and nondifferentiable optimization problem, whose feasible set may be not connected in some cases and constraint region is generally not polyhedral for m ≥ 3. Finally, the SOCBLP in the optimistic case is reformulated as a single level optimization problem by using the KKT conditions for the lower level problem.
Zhou et al. [18] formulated the dynamic OD estimation problem as a single level nonlinear optimization model, solved with a relaxation algorithm of the lagrangian extension of the original one, taking into account route choice in order to work in the path- flow dimension.
OptORF is formulated as a single level mixed integer linear program (MILP) by replacing the inner maximization problem with its optimality conditions as constraints.
The other possible explanation is that gene expression as a single level of genomic data is insufficient to explain the clinical outcomes of interest since cancer can be dysregulated by multiple alterations through genome, epigenome, transcriptome, and proteome levels.
The other possible explanation is that gene expression as a single level of genomic data is insufficient to elucidate the clinical outcome since cancer can be dysregulated by multiple alterations through genome, epigenome, transcriptome, and proteome levels [ 10].
In this calculation, we treated E and A as a single level [ 20] because the lifetime of E (~30 ns) is almost 10 times shorter than the time-scale for non-radiative decay from A to A (~300 ns).
