Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: A Unified Approach to the Global Exactness of Penalty and Augmented
  Lagrangian Functions I: Parametric Exactness   In this two-part study we develop a unified approach to the analysis of the
global exactness of various penalty and augmented Lagrangian functions for
finite-dimensional constrained optimization problems. This approach allows one
to verify in a simple and straightforward manner whether a given
penalty/augmented Lagrangian function is exact, i.e. whether the problem of
unconstrained minimization of this function is equivalent (in some sense) to
the original constrained problem, provided the penalty parameter is
sufficiently large. Our approach is based on the so-called localization
principle that reduces the study of global exactness to a local analysis of a
chosen merit function near globally optimal solutions. In turn, such local
analysis can usually be performed with the use of sufficient optimality
conditions and constraint qualifications.
  In the first paper we introduce the concept of global parametric exactness
and derive the localization principle in the parametric form. With the use of
this version of the localization principle we recover existing simple necessary
and sufficient conditions for the global exactness of linear penalty functions,
and for the existence of augmented Lagrange multipliers of Rockafellar-Wets'
augmented Lagrangian. Also, we obtain completely new necessary and sufficient
conditions for the global exactness of general nonlinear penalty functions, and
for the global exactness of a continuously differentiable penalty function for
nonlinear second-order cone programming problems. We briefly discuss how one
can construct a continuously differentiable exact penalty function for
nonlinear semidefinite programming problems, as well.

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The categories of this paper are: hep-lat
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The categories of this paper are: hep-ph
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The categories of this paper are: q-fin
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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: nucl-th
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The categories of this paper are: solv-int
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The categories of this paper are: eess
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The categories of this paper are: cond-mat
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The categories of this paper are: astro-ph
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The categories of this paper are: bayes-an
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The categories of this paper are: adap-org
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The categories of this paper are: alg-geom
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The categories of this paper are: physics
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The categories of this paper are: quant-ph
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The categories of this paper are: hep-th