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The security analysis demonstrates how privacy and security constraints are solved by the framework.
Both non-linear optimization problems with constraints are solved by the downhill simplex method including a penalty function.
Representative examples of shape and topology optimization with and without stress constraints are solved with success demonstrating the advantages of the FCM/LSF method.
The size effect is considered by the material length scale factor l, the shape asymmetry is taken into account using the non-prismatic bending stiffness Bm(x), and the bilateral constraints are solved using an energy method that minimizes the total energy of the deflected microbeams.
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Other important algorithmic approaches include sequential quadratic programming, in which an approximate problem with a quadratic objective and linear constraints is solved to obtain each search step; and penalty methods, including the "method of multipliers," in which points that do not satisfy the constraints incur penalty terms in the objective to discourage algorithms from visiting them.
Then the optimization problem with color channel constraints is solved by using the classical gradient technique.
Once the gas network optimization with security constraints is solved, Benders' cuts (18) are added to the master problem.
The selected set of constraints is solved numerically and an improved model is rebuilt from the solution.
In our system, the combination of soft and hard constraints is solved using the Lagrange multiplier method.
For the electricity network a unit commitment problem with optimization of energy and reserves under a power pool, considering all system operational and unit technical constraints is solved.
The discrete optimal design problem, formulated under strain and ply contiguity constraints is solved using evolution strategies, a guided random-search method.
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