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By analyzing the structure of the optimal beamforming matrix, the optimization problem is simplified so that it can be directly solved using the genetic algorithm (GA).
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The polygon boundaries are directly solved using a pre-calculated mean-value interpolation.
As the gain matrix in (13) always has a very small condition number, it can be directly solved by using the Cholesky decomposition and conventional forward/back substitutions; note that (12) is a quadratic programming (QP) problem, and it also can be solved by CPLEX.
This situation is directly solved by the proposed methodology.
Both of these optimization problems are convex: the first one can be solved using proximal splitting methods, while the second one can be solve directly in terms of a matrix inversion.
which can be solved using, e.g., the SpaRSA algorithm[30] that is directly capable to deal with complex data.
All Area Mazes can be solved using only whole numbers.
These problems can be solved using barcode sequences.
The chemical species concentration equation is solved using primitive variables and local fluxes are locally directly calculated at the interface.
The energy equation is solved using a diffuse-interface method, which avoids the need to apply the thermal boundary conditions directly at the solid front.
The problem then was solved using VNS.
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Justyna Jupowicz-Kozak
CEO of Professional Science Editing for Scientists @ prosciediting.com