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Yet the problem is simple to solve.
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The dual problem is simpler to solve and its solution can be used to recover primal variables (Section "Recovery of optimal primal variables") with reduced computational complexity due to the inherently separable structure of the problem Lagrangians (Section "Separability").
(2004) extended the fuzzy approach of Abo-Sinna (2001) for solving non-linear bi-level and tri-level multiobjective decision making under fuzziness by defining a membership function of each objective function and control variable of each decision maker to formulate a single level programming problem which is simpler to solve than the original problem.
The basic strategy of inversive methods is to transform a given Apollonius problem into another Apollonius problem that is simpler to solve; the solutions to the original problem are found from the solutions of the transformed problem by undoing the transformation.
Moreover, we choose to use these constraints explicitly instead of adding them to the objective function (using Lagrangian multipliers), as this formulation is simpler to solve in our optimization procedure.
The ECC requires the elliptic curve discrete logarithm problem being simple to solve.
On the other hand, macroscopic averaged equations are simpler to solve and by the very nature of their construction may be scaled up for the system level (up to the length scale of bioreactors) optimization.
The problem is simple to pose, yet tough to solve.
The current problem is simple to state but difficult to solve: officials expect that tax revenues and state and federal aid will fall roughly $5 billion short of meeting the city's expenses next year.
The equation is simple to formulate but is challenging to solve when the number of Lambertian surfaces associated with an application becomes large.
And unlike many issues related to climate change, it's one which is incredibly simple to solve.
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Justyna Jupowicz-Kozak
CEO of Professional Science Editing for Scientists @ prosciediting.com