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************ Corrections/changes made in second printing, July 1997 **********
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************ Typos ****************
Corrected answers to ex31, ex39, ex144.
p.9 l.-8, 'overbook' changed to 'overbooked'.
p.23 l.11, 'minimize' changed to 'maximize' in Exercise 2.9.
p.23 l.12, first minus sign aligned with plus signs above and below.
p.30 l.-4, '2 eps' changed to '2.5 eps'.
p.40 l.7, underline extended.
p.79, subpart enumeration in exercise 5.12 corrected (was 1,2,1,2,3).
p.104 l.3, 'x6' changed to '2 x6'.
p.111 l.-4, 'constraints' made possessive with an apostrophy.
p.154 l.8, 't_1' changed to 't_2'.
p.160 l.11, '' changed to ``.
p.175 l.-2, ended the sentence with a period. fixed alignment of eqn number.
p.265 l.4, changed 'a/mu' to 'mu/a'.
p.281 l.19, changed 'A xbar + wbar' to 'A^T ybar - zbar'.
p.282 l.8, corrected k-th term of Taylor expansion.
p.335 l.2, changed 'there exists' to 'there exist'.
p.392 l.-1, Y^{-1} changed to Y^{-1}e.
p.264 l.-2, replaced x by w, z-bar by y-bar, and j by i.
p.382 l.7,8, reversed the signs of the $mu X^{-1} e$ and $mu Y^{-1} e$ terms.
p.383 l.8,9, reversed the signs of the $mu X^{-1} e$ and $mu Y^{-1} e$ terms.
**** Changes/Enhancements *********
Added answers for ex84, ex85, ex185, ex180, ex190.
p.80 l.-8, 'theorem 5.2' changed to 'theorem'.
p.87 l.-14,-15, 't' changed to 'the maximum'.
p.113 l.8-11, 'characterizing each of ...' changed to 'for detecting
infeasibility and/or unboundedness in the primal--dual simplex method.
p.161 l.-3, 'optimal solution' changed to 'objective value of the optimal
solution'.
p.162 l.10, Inserted following sentence:
'Suppose that $\xi^*(b) < \infty$ for all $b$.
Also, added the explicit definition of concavity.
p.195 l.-7, added index entries for Gonin, Money, Dodge.
p.195 l.-6, added reference to Bloomfield-Steiger book.
p.195 l.-1, added index entries for Adler and Berenguer.
p.266 l.-1, changed "standard form" to "equality form".
p.280 l.-16, added specification of \delta=1/10 and r=9/10 to problem statement.
******** Layout Adjustments *******
p.38 l.-0, removed pagebreak.
p.176 l.4, fixed alignment of eqn number.
p.215 l.4, changed the em dash to an en dash.
p.266 l.-10,-12, converted displayed equations to inline.
p.267 l.2,7, fixed alignment of eqn number.
p.281 l.20, fixed alignment of eqn number.
p.281 l.-1, enlarged the parens.
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************ Corrections/changes made in third printing, Jan 1998 **********
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p.xvii l.-14, 2^n changed to 2^n - 1.
p.18 l.-1 'in the previous chapter' changed to 'earlier in this chapter'.
p.43 l.-6, strict inequalities made not strict.
p.48 l.-6, enlarged parens.
p.49 l.7, strict inequalities made not strict.
p.57 l.10-11, 'as we saw earlier' deleted.
p.109 l.-9, 'b^T y_N^*' changed to 'c_B^T B^{-1} b'.
p.207 l.9-10,18 'Chapter 6' changed to 'Chapter 7'.
p.222 l.5 'a network' changed to 'a possibly disconnected network'.
p.228 l.-9 'two arrays index by' changed to 'two arrays indexed by'.
(For pagination, also need to replace p.229.)
p.282 l.8, deleted extraneous '+' sign in Taylor expansion.
p.283 l.2, changed 'a sequence of nonnegative real numbers' to 'a sequence of
real numbers between zero and one'.
p.286 l.11, replaced 'a again' with 'again'.
p.372 l.13, maximization problem changed to minimization by negating.
p.372 l.8-9, parens enlarged.
(For pagination, also need to replace p.373.)
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************ Corrections/changes scheduled for the fifth printing **********
************ Changes sent to Kluwer in Oct 1998 **********
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p.8 l.-1-2, Deleted the three parenthetical statements.
p.9 l.4,5,6, Deleted the three parenthetical statements.
p.25 l.4 and l.-2, 'entering' changed to 'leaving'.
p.34 l.-6, "For an arbitrary linear program" changed to "For an arbitrary
linear program in standard form".
p.56 l.9-10, "This was undoubtedly true in the case of Gaussian elimination,
and it is true here as we explain the strong duality theorem."
changed to
"Anyone who has taken a course in linear
algebra probably already appreciates such a statement.
In any case, it is true here as we explain the strong duality
theorem."
p.107 l.5, +x_1 term added.
p.160 l.-5, '(10.10)' changed to '(10.9)'.
p.224 l.-3, unboxed '3' changed to '-4'.
p.261 l.5, changed 'each \xi satisfying' to 'each \xi \ne 0 satisfying'.
p.270 l.-9, 'Dz' changed to 'Dw'.
p.282 l.-7, 'Dy' changed to 'Dz'.
p.285 l.9, 'Dz' changed to 'Dw'.
p.324 bibliographic info added for Theorem 20.1.
Corrected answer to Exercise 2.1.
p.405 Answer to 7.1(3) changed to (0,8,0,0,0,10,10).
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************ Changes made but not sent to Kluwer yet **********
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p.174 l.-11, changed 'describe' to 'described'.
p.244 figure 15.2, changed 'u_i' to 'v_i' to make consistent with text.
p.288 l.-8, added an 'e' just before the last right paren.
p.290 l.3,5, changed 'x_feas' to 'x_opt'.
p.301 l.-6, a '2' is added to the matrix to make it symmetric as it's supposed
to be.
p.302 l.7, a '2' is added to the same place in this matrix.
p.387 l.2, added an '=' sign in equation 23.8. Also, deleted the extraneous Dy
at end of 2nd row of rhs.
p.391 l.-2, multiplied equation by wi + Dwi to clear the denominator.
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************ Corrections/changes for the 2nd edition **********
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Changed the font of basic and nonbasic indices to caligraphic to
avoid confusion with basic and nonbasic submatrices.
Chapters 6,7,8 changed (y_1,y_2,...,y_{n+m}) to (z_1,z_2,...,z_{n+m})
throughout.
Shortened the "Notes" section at the end of Chapter 6.
p. 39 l.4-6, "when it is solved by the simplex method" changed to
"its initial dictionary is not degenerate and, when solved
by the simplex method"
p. 247 l.7 right paren moved in front of equals sign.
p. 310 paragraph on predictor-corrector moved to p. 345.
To do:
Define argmax, min operator, max operator.
Make clear the relation between B^{-1}N from primal and corresponding
expression from dual.
For planar graphs show that the dual network simplex method is
precisely the primal network simplex method on the dual graph.
Add complexity calculation to Dijkstra's algorithm.