On second order conditions for equality constrained extremum problems

We prove a relationship between the bordered Hessian in an equality constrained extremum problem and the Hessian of the equivalent lower-dimension unconstrained problem. This relationship can be used to derive principal minor conditions for the former from the relatively simple and accessible condit...

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Vydáno v:Economics letters Ročník 121; číslo 3; s. 440 - 443
Hlavní autor: Mandy, David M.
Médium: Journal Article
Jazyk:angličtina
Vydáno: Amsterdam Elsevier B.V 01.12.2013
Elsevier Science Ltd
Témata:
Economic analysis
Economic conditions
Economic theory
economics
Equality
Hessian
Mathematical analysis
Mathematical problems
Matrix
Minors
Optimization
Studies
C60
Hessian
Optimization
Minors
ISSN:0165-1765, 1873-7374
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Shrnutí:We prove a relationship between the bordered Hessian in an equality constrained extremum problem and the Hessian of the equivalent lower-dimension unconstrained problem. This relationship can be used to derive principal minor conditions for the former from the relatively simple and accessible conditions for the latter. •Establishes a simple relationship between a Hessian and bordered Hessian.•Derives necessary and sufficient second order conditions from this relationship.•The only proof that avoids use of quadratic forms subject to side conditions.•Clarifies Samuelson’s “great loss of symmetry”.
Bibliografie:SourceType-Scholarly Journals-1
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ISSN:0165-1765
1873-7374
DOI:10.1016/j.econlet.2013.09.017