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This problem entails solving a high dimensional optimization problem.
This is a high dimensional optimization problem with black-box nonconvex objective function.
To deal with the potential high dimensional optimization problem (i.e. large transition matrices), an enhanced offspring generation procedure is proposed to help the ES algorithm converge efficiently and find better Pareto frontiers through generations.
To avoid the infinite dimensional optimization problem, the proposed parameter-dependent co-design condition is relaxed as a finite set of linear matrix inequalities at the polytope vertices, which can be numerically trackable and computationally efficient.
This means that (2) is an infinite dimensional optimization problem which in principle could be difficult to solve.
Thus, for a given channel coefficient vector the applied weight is found after solving the finite dimensional optimization problem (2).
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To establish the sensitivity of final state specification on optimal control of nonlinear systems, the problems are transformed into finite dimensional optimization problems suitable for nonlinear programming (NLP).
High dimensional optimization problems play an important role in many complex engineering area.
The improvement in correspondence between measured and modeled hydrographs confirmed the reliability of the combination of GSA and PSO in dealing with highly dimensional optimization problems.
The objective is determining an optimal step ξopt that solves the following one-dimensional optimization problem: (30) min ξ C T L = C T (x k + ξ d k ) Subject to ξ > 0, h i (x k + ξ d k ) ⩽ 0, i = 1 … N c, where C T L is the total costs function along the search direction.
In order to find the optimal film distance, I treated this as a one-dimensional optimization problem over a unimodal function.
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Justyna Jupowicz-Kozak
CEO of Professional Science Editing for Scientists @ prosciediting.com