Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Introduction to Nonsmooth Analysis and Optimization   This book aims to give an introduction to generalized derivative concepts
useful in deriving necessary optimality conditions and numerical algorithms for
infinite-dimensional nondifferentiable optimization problems that arise in
inverse problems, imaging, and PDE-constrained optimization. They cover convex
subdifferentials, Fenchel duality, monotone operators and resolvents,
Moreau--Yosida regularization as well as Clarke and (briefly) limiting
subdifferentials. Both first-order (proximal point and splitting) methods and
second-order (semismooth Newton) methods are treated. In addition,
differentiation of set-valued mapping is discussed and used for deriving
second-order optimality conditions for as well as Lipschitz stability
properties of minimizers. The required background from functional analysis and
calculus of variations is also briefly summarized.

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The categories of this paper are: cond-mat
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The categories of this paper are: cs
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The categories of this paper are: physics
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The categories of this paper are: dg-ga
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The categories of this paper are: chem-ph
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The categories of this paper are: atom-ph
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The categories of this paper are: ao-sci
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The categories of this paper are: plasm-ph
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The categories of this paper are: chao-dyn
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The categories of this paper are: comp-gas
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The categories of this paper are: stat
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The categories of this paper are: funct-an
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The categories of this paper are: gr-qc
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The categories of this paper are: hep-th
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The categories of this paper are: nucl-ex
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The categories of this paper are: hep-ex