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Subproblems (4.7) and (4.8) can then be solved efficiently, for example, by the Matlab optimization toolbox.
Hence, the contracting model can be solved efficiently for a general number of retailer types.
The subproblems in Algorithm 3.2 can be solved efficiently, for example, by using MATLAB Optimization Toolbox R2008a.
From Lemma 2, (P4 τ ) is a convex problem; therefore, it can be solved efficiently for an optimal solution.
Especially we show that the M2CP problem can be solved efficiently for a class of influence propagation models.
This formulation can be applied to areas such as document clustering [26] and can be solved efficiently for very large m and n [30].
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The methodology leads to a set of linear algebraic equations that are solved efficiently for the unknown nodal displacements.
Since such heuristic-based approach uses convex optimization, the joint admission control and power allocation problem can be solved efficiently even for large networks.
Non-linear prediction models, like artificial neural networks (e.g., NetMHC [ 3]), or even more complex prediction approaches like the one proposed by Zhang et al. [ 19], would lead to a non-convex, non-linear mixed integer optimization problem that cannot be solved efficiently and optimally even for small instances [ 20].
In addition, the corresponding nonlinear equations can be solved efficiently using Picard iterations, even for highly stretched boundary layer meshes.
It is well known that differential equations in one dimension can be solved efficiently with Chebyshev discretizations, O(N) operations for N unknowns, however this efficiency is lost in higher dimensions due to the coupling between modes.
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Since I tried Ludwig back in 2017, I have been constantly using it in both editing and translation. Ever since, I suggest it to my translators at ProSciEditing.

Justyna Jupowicz-Kozak
CEO of Professional Science Editing for Scientists @ prosciediting.com