Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: On the Characterization of Generalized Derivatives for the Solution
  Operator of the Bilateral Obstacle Problem   We consider optimal control problems for a wide class of bilateral obstacle
problems where the control appears in a possibly nonlinear source term. The
non-differentiability of the solution operator poses the main challenge for the
application of efficient optimization methods and the characterization of
Bouligand generalized derivatives of the solution operator is essential for
their theoretical foundation and numerical realization. In this paper, we
derive specific elements of the Bouligand generalized differential if the
control operator satisfies natural monotonicity properties. We construct
monotone sequences of controls where the solution operator is G\^ateaux
differentiable and characterize the corresponding limit element of the
Bouligand generalized differential as being the solution operator of a
Dirichlet problem on a quasi-open domain. In contrast to a similar recent
result for the unilateral obstacle problem [RU19], we have to deal with an
opposite monotonic behavior of the active and strictly active sets
corresponding to the upper and lower obstacle. Moreover, the residual is no
longer a nonnegative functional on H^{-1} and its representation as the
difference of two nonnegative Radon measures requires special care. This
necessitates new proof techniques that yield two elements of the Bouligand
generalized differential. Also for the unilateral case we obtain an additional
element to that derived in [RU19].

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The categories of this paper are: dg-ga
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The categories of this paper are: physics
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The categories of this paper are: hep-ex
30
The categories of this paper are: q-alg
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The categories of this paper are: acc-phys
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The categories of this paper are: econ
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The categories of this paper are: math-ph
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The categories of this paper are: comp-gas
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The categories of this paper are: hep-lat
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The categories of this paper are: chem-ph
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The categories of this paper are: nlin
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The categories of this paper are: q-bio
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The categories of this paper are: adap-org
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The categories of this paper are: funct-an
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The categories of this paper are: solv-int
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The categories of this paper are: cond-mat