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First the sizing of the process without constraint is solved.
After that, the constraint is solved in order to obtain the Lagrange multiplier.
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Bidding with transmission constraint was solved in [11, 12, 13].
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.
The rapid modeling formulation with a non-linear objective function subject to non-linear constraints is solved by the differential evolution algorithm.
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Justyna Jupowicz-Kozak
CEO of Professional Science Editing for Scientists @ prosciediting.com