Following is a list of typos (more like questionable items) in the text:
Numerical Optimization, by
Jorge Nocedal, and
Stephen Wright, 1999,
Springer Verlag.
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On page 16, the definition of positive definite and positive
semidefinite does not include B=BT whereas the definition in
the appendix correctly does state that the matrix A is symmetric, see
page 594.
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On page 24, in the equation above (2.15), the Hessian should be at
xk rather than at xk+1, i.e. that is what follows from the
Taylor series. Then the approximation is done for Bk+1.
Alternatively, the Taylor series is approximated at xk+1 in
the direction (xk-xk+1).
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Page 47, above (3.24), the gradient at xk changed notation to gk
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In problem 3.2 on Page 62: as stated, it is unclear whether the
constants c1,c2 are given or are to be shown to
exist. In fact, there exist functions for which any choice of
constants 1>c1>c2>0 result in no (Wolfe) step
lengths. However, there also exist functions where any choice of
constants 1>c1>c2>0 result in (Wolfe) step.
(
see comments)
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In problems 3.3 and 3.4 on Page 62, the term strongly convex quadratic
is used. For a quadratic, strictly convex is equivalent.
It is unsure that the terms are defined somewhere in the text.
The definitions can be found e.g.
at the Mathematical Programming glossary:
http://carbon.cudenver.edu/~hgreenbe/glossary/S.html
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Page 69, paragraphing error in the middle of the page (due likely to
missing end-center in latex)
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Page 133: In problem 5.4, the assumption that the vectors p_0 to p_{k-1}
are linearly independent is missing. (These vectors were conjugate
directions in previous questions.)
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Page 156: The comment about large-scale situations for trust-region
subproblems has changed. There are now codes that will solve the
large-scale case using a Lanczos approach, i.e. it is no longer
necessary to sovle several linear systems per iteration, but rather
employ a 'restarted' Lanczos eigenvalue routine. See e.g. the following
references (and the references cited therein):
-
A Survey of the Trust Region Subproblem within a Semidefinite Framework,
(Master's thesis of Charles Fortin, supervisor Henry Wolkowicz)
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A Semidefinite Framework for Trust
Region Subproblems with Applications to Large Scale Minimization,
Franz Rendl and Henry Wolkowicz, Math Progr 1997, vol 77, Mathematical Review
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author = "N. GOULD and S. LUCIDI and M. ROMA and
Ph. L. TOINT",
TITLE = {Solving the trust-region subproblem using the {L}anczos
method},
JOURNAL = siopt,
VOLUME = {9},
number = {2},
YEAR = {1999},
PAGES = {504--525}
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author = "S.A. SANTOS and D.C. SORENSEN",
title = "A new matrix-free algorithm for the large-scale
trust-region subproblem",
institution = "Rice University",
year = "1995",
type = "Technical Report",
number = "TR95-20",
address = "Houston, TX"}
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author = "W.W. HAGER",
title = "Minimizing a quadratic over a sphere",
institution = "University of Florida",
year = "2000",
address = "Gainsville, Fa"}
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Page 269, 3/4 of the way down:
The sum is over i, but should be over j.
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Pages 320-322: The discussion here that derives a Lagrange multiplier
condition does not assume a constraint qualification. The discussion
seems to imply that the results are true without a constraint
qualification, but this clear fails e.g. if \nabla c_1(x)=0 but
\nabla f(x) \neq 0.
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Page 398, the equation above equation (14.7) has
s and
out of order.
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Page 401, the equation (14.15) has
rb and rc out of order.
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Page 406, extra comma in 3rd line from the bottom in the expression for
RHS.
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Page 487, Problem 16.4: Remove the words at the start of the problem "Use
Theorem 12.6". The problem asks to "show that the second-order
sufficient conditions hold". But Theorem 12.6 uses the second-order
conditions to prove optimality. Perhaps what is meant is:
"show that the second-order sufficient conditions from Theorem 12.6
hold".