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Exact(8)
where λ opt is an optimum solution to Eq. ( 12 ).
Hence x ¯ is an optimum solution for (P) and the theorem is proved.
First, we need to prove that the characteristic function ({chi }_{O} of O = text {DCC}_{G_{le }^{T}}(s_{i})) is an optimum solution in (mathcal {X}_{infty }^{text {in}}({s_{i}},{mathcal {S}}_{{b}})).
There is an optimum solution for (20), where arg max i { Γ i | i ∈ W } is involved in a valid combination, if there exists at least one valid combination.
Also, assume that { Γ a 1, Γ a q } is found as a valid pairwise combination by Algorithm 1. From Lemma 1, we know there is an optimum solution, where Γ a 1 is involved in a valid combination.
Let l = arg max i { Γ i | i ∈ W }. If there is an optimum solution that does not use l in any valid combination, then swapping l with any element involved in any valid combination found will not affect the optimality of the solution.
Similar(52)
"Whether it's an optimum solution in terms of a health care delivery network for Manhattan, I am not sure," said Stephen Berger, chairman of the now-defunct state Commission on Health Care Facilities in the 21st Century.
The self-powered gas sensing system based on NGs will be an optimum solution.
It is also possible to define a particular location of the shortened window, but it may not necessarily be an optimum solution.
He said: "There have been a number of discussions with several grounds and local clubs and we are very close to finalising what we trust will be an optimum solution for the club in both financial terms as well as the level of facilities available next season.
These arcs were removed in Step 2 of the algorithm and, therefore, have no values greater than ({varepsilon }_{infty downarrow }^{text {in}}), so the characteristic function of (text {DCC}_{G_{le }^{T}}(s_{i})) must be an optimum solution in (mathcal {X}_{infty }^{text {in}}({s_{i}},{mathcal {S}}_{{b}})).
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Justyna Jupowicz-Kozak
CEO of Professional Science Editing for Scientists @ prosciediting.com