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The first posed problem satisfied all constraints, so it must be meaningful.
We identify the problem satisfied by the limit ((u,w)) of the sequence of optimal pairs ({ (u_{varepsilon},w_{varepsilon}) } _{varepsilon}), where (u_{varepsilon}) denotes the state of the system to be controlled, and also the problem satisfied by the limit p of ({ p_{varepsilon} } _{varepsilon}).
Consider the following particular case of problem (7) with (f(0)=0), (g(0)=0), f and g increasing, and the hypothesis for a unique global solution of the following problem satisfied in Theorem 2.2.
Therefore, van Roomen's solution which uses the intersection of two hyperbolas did not determine if the problem satisfied the straightedge-and-compass property.
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In the case discussed here where the solution is expected to be spatially sparse, CS uses the insight that the most spatially sparse solution satisfying Eq. (1) is the exact solution with high probability (if the problem satisfies the necessary conditions [ 4, 5]).
By a Boland-Nicolaides argument, we prove that the discrete saddle-point problem satisfies a Babuška-Brezzi inf-sup condition.
Assume that the solution of the PDAC problem satisfies inequalities.
When a posed problem satisfies no constraint, the problem is meaningless.
(ii) It is easy to see that the problem satisfies the assumptions of Theorem 9.
According to the analytical results, a solution to the problem satisfies where is a root of.
(i) It is easy to see that the problem satisfies the assumptions of Theorem 8.
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Justyna Jupowicz-Kozak
CEO of Professional Science Editing for Scientists @ prosciediting.com