Following is a list of typos (and questionable items) in the text:
Numerical Optimization, by
Jorge Nocedal, and
Stephen Wright, 1999,
Springer Verlag.
(Thanks go to the graduate students and the auditors in the course.)
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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).
Also: the third line above (2.15); it should be the
Hessian, not the gradient.
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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 on homework solutions)
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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 78: In Theorem 4.3, the primal feasibility condition on
p* is missing.
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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):
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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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Pages 258-259: There is a problem with
x* below equation (10.17) on page 258. There
should be a minus in front of the right-hand-side.
The next two formulae should be updated appropriately.
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Page 286, equation (11:20): The LHS is a vector while the RHS is a
scalar. It appears that the norm of the LHS is intended to be <= to the
RHS.
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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 339: the second sentence following "INTRODUCING LAGRANGE
MULTIPLIERS" on page 339 does not make appear to make sense.
Possibly < 0 should read \geq 0. Note that the linearizing cone
F1 contains the tangent cone.
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Page 486, exercise 16.1: This is a quadratic maximization
program but the objective is strictly convex. I assume that
minimization is intended.
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Page 579 (A.3): the RHS is actually the span. This will
differ if 0 is not in the affine hull. The true definition of
affine combinations are those that are linear combinations
whose coefficients add up to 1, i.e.
{z: z=ax+by, for all x,y in F, and for all a,b with a+b=1}
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Page 398, the equation above equation (14.7) has
s and
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 424, second line after (15.2): increasing should read
decreasing.
"exact penalty function" is used but not explained.
sentence starting with "In barrier methods":
"but approach zero" should read "but approach infinity".
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page 435, between (15.25) and (15.26): referring to the
ell_2 norm is pointless as it is not used.
(15.26): A(x) refers to the Jacobian of the constraint function c(x)
last sentence: grammatically wrong: "constraints
are MORE AND MORE penalized by decreasing mu"
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page 437, top half: psi should be replaced twice by phi.
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page 495, in Framework 17.1: The tolerance $\tau_{k+1} needs to be
updated (specified).
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Page 509, Theorem 17.4, iii: The Hessian
\nabla^2 P(x(\mu),\mu) is positive definite, i.e. $x(\mu)$ not $x$.
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Page 575, Problem 18.2: The starting point and the solution are
exchanged.
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Page 614, Reference [57]: It should be "G. F. Corliss", not "B. F. Corliss".