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As our experiments showed, indeed there are many cases where we have infeasible problems.
These results globally confirm the need to establish a negotiation procedure with the users for preventing infeasible problems.
However, since CAC is out of scope of this paper, we do not consider dropping users should the available resources not satisfy the minimum requirements of all users (out of 1000 channel realisations, around 10% led to infeasible problems).
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If no solution exists, then the decision makers realize it is an infeasible problem formulation.
Note that if the intersection is empty, the SDP algorithm returns infinity to indicate an infeasible problem. Figure 5 CDF comparison of relative tightness for POCS position error for Gaussian measurement errors ( σ =1 [m], N=15), (a) ρ = σ, (b) ρ =2 σ, (c) ρ =3 σ, and (d) ρ =4 σ.
We subsequently modify the algorithm to sub-divide locally by utilizing information from infeasible linear problems.
In addition, in order to reduce the incidence of infeasible LP problems, I employ multi-year "window" data as the reference technology.
Although I employed multi-year "window" data as the reference technology, due to infeasible LP problems, I could not obtain results for Tottori Prefecture in the Chugoku region and Kochi Prefecture in the Shikoku region.
To prevent infeasible LP problems, the lower constraints on the ATP maintenance reactions (ATPM, BTATPM, MMATPM) were set to 0 mmol.gDw−1.hr−1.
By introducing the violation parameter, the former infeasible optimisation problem turns into a feasible one.
To our knowledge, this is the best iteration complexity obtained so far for an infeasible SO problem.
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Justyna Jupowicz-Kozak
CEO of Professional Science Editing for Scientists @ prosciediting.com