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Jeyakumar et al. [11] have established some necessary and sufficient conditions for a given feasible point to be a global minimizer of some minimization problems with mixed variables.
We derive lower bounds on the black-box oracle complexity of large-scale smooth convex minimization problems, with emphasis on minimizing smooth (with Hölder continuous, with a given exponent and constant, gradient) convex functions over high-dimensional ∥⋅∥p-balls, 1≤p≤∞.
Hiriart-Urruty [20] studied global optimality conditions for quadratic minimization problems with quadratic constraints.
Moreover, the work in [24-26] [24-26]red the power minimization problems with outage probability considereds.
These problems can be formulated as minimization problems with non-convex constraints.
In Section 3, we provide some global optimality conditions for nonlinear minimization problems with box constraints, and deduce necessary and sufficient optimality conditions for a class of nonconvex quadratic minimization problems with box constraints.
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We model the cold supply chain design problem as a mixed-integer concave minimization problem with dual objectives of minimizing the total cost - including capacity, transportation, and inventory costs - and the global warming impact.
The performance function minimization problem with polynomial matrix inequalities is then transformed into a problem of minimizing a convex performance function involving standard LMIs.
Figure3c depicts an example of ED for a minimization problem with two objectives.
Power allocation is modeled as a minimization problem with three practical constraints.
Figure3a presents an example of C indicator for a minimization problem with two objectives.
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