Errata to the 3rd printing (9 8 7 6 5 4 3 in ISBN number page) of: Jorge Nocedal and Stephen J. Wright: "Numerical Optimization", 2nd ed. Springer-Verlag, 2006. Miguel A. Carreira-Perpinan, 2010. - "strongly convex function" appears in several places (eg exercises 3.3, 3.4, 6.1) but is never defined. - P. 71: . l. 5: "-g_k." . l. -3: wrong indentation. - P. 84 l. 10: three factorizationS. - P. 143 l. 14: "the the". - P. 179 Alg. 7.5: yk = should use <-. - P. 236 alg. 9.3: wrong indentation of "for" loop; pi = ei should use <-. - P. 237 l. -2: conjugate-gradient -> conjugate-direction. - P. 238: centroid should be (1/n)\sum{x_i}. - P. 296 l. 12: remove "rather". - P. 344: n should be m in eq. (12.84) (\lambda \in R^m), and in l. 3. - P. 348: eq. after (12.90): max should be over \lambda and x. - P. 349: eq. after (12.93) should have no transpose after the inverse G. - P. 358 l. 17: "make derivation" -> "makes derivation". - P. 388 l. 13: close parenthesis. - P. 396 l. 1: "toward the a". - P. 399 l. 6: "Mopreover". - P. 482ff: r_d and r_p (the residuals for vectors c and b) might be called r_c and r_b (as in ch. 14). - P. 517: last line and following lines in next page: k should be \mu_k (an easier proof for the 2nd-order conditions is obtained by writing w = u + v, where u \in null(A) and v is orthogonal to u). - P. 530: chapter 14 -> 19. - P. 532: algorithm 18.1 needs "k <- k + 1". - P. 564ff: the use of the slack variables and their associated Lagrange multipliers is a bit unclear (this also happens in earlier discussions of interior-point methods). To get eqs. (19.2) one needs to apply the KKT conditions to the problems without slacks s and introduce s afterwards (otherwise, the constraint s >= 0 needs its own Lagrange multipliers). In eqs. (19.5) I can't see how to get rid of the Lagrange multipliers for s. In eq. (19.7), the Lagrangian ignores the inequality (19.1). - P. 595: 19.5a: "thatensure". - P. 609 l. 8: A -> Q. - P. 627 l. 2: "of his matrix" -> "of this matrix". - P. 648: ref. 239 should be Computer Journal 7 (1964), pp. 155-162. - P. 603 l. -14: the definition given is not for the direct sum \oplus of A and B, but for their sum. Errata to the 6th printing (9 8 7 6 in ISBN number page) of: Jorge Nocedal and Stephen J. Wright: "Numerical Optimization". Springer-Verlag, 1999. Miguel A. Carreira-Perpinan, 2005. - P. 5 fig. 1.2: should be x13. - P. 19, l. 2: *have* seen. - P. 24 l. -9 (displayed eq.): the Hessian should be at k (not k+1), or one should add and subtract Hessian(x+p)*p to the displayed eq. before. - P. 24 l. -8: "within which *the Hessian* is positive definite" (not the gradient). - P. 31, end of exercise 2.8: "...find all minimizers of the problem (2.9)". Some students think (2.9) refers to exercise (2.9) (next line) rather than equation (2.9) in page 19. - P. 40, fig. 3.5: the points of tangency are slightly offset wrt their corresponding dotted vertical line, which obscures the mean value theorem argument. - P. 117 eq. before 5.35: lambda_1 and lambda_n should be exchanged. - P. 117 l. -3: 3.28 -> 3.29. - P. 120, alg. 5.4: the use of = and \leftarrow is inconsistent. - P. 123, eq. 5.46: x -> x^*. - P. 165 l. -5: infintesimal. - P. 260: f_k should be r_k in l. 1 (Jk*fk -> Jk*rk) and eq. 10.22. - P. 271 l. -1 (eq. 10.43): w^2_i -> w^2_j. - P. 220, exercise 8.1: (a) Strict (strong) convexity hasn't been defined in the book I think. Also, a positive Hessian implies strict convexity but not vice versa (eg f(x)=x^4 at x=0). Instead of using the Hessian, a more general proof can use the first-order strict convexity conditions f(y) > f(x) + (book by Boyd & Vandenberghe, p. 69ff). (b): g is not defined and students confuse it with the gradient. - P. 332, eq. (12.34): "lim... -> d", the arrow should be an equals sign: "lim... = d" - P. 339, def. 12.4: alpha is not necessary to define F1. - P. 358, exercise 12.4: maybe say explicitly these are two different functions; the second one looks like a rewriting of the Inf-norm with a missing absolute value. - P. 424, l. 9: increasing -> decreasing. - P. 424, l. -13: "but approach *zero* as x approaches the boundary" -> infinity. - P. 433: after eq. (15.22), the minimum-norm problem should be min \norm{x}_2 s.t. Ax=b rather than min \norm{Ax-b}_2. - P. 435, eq. (15.26): A(x) has not been defined. - P. 442-443 (portfolio optimization example): in usual statistical notation, the covariance matrix is matrix G while the matrix with entries \rho_{ij} is a correlation matrix. - P. 442: displayed equation after eq. (16.2): E(R) -> E[R]. - P. 454, l. -8: "linearly dependent" -> "linearly independent". - P. 462, algorithm 16.1: . The line "set \hat{W} = W_k" is unnecessary. . Just before "else (* p_k \neq 0 *)": "x_{k+1} = x_k" -> leftarrow instead of equals sign. . "obtain W_{k+1} by ... to W_{k+1}" -> to W_k. - P. 465, 2 lines before heading "Further remarks...": \hat{\lambda_i} should be 0.8, not 1.25. - P. 482, l. 3: "slack vector y" -> "surplus vector y" (for consistency with eq. (13.2) in p. 365). - Ch. 17: most figures have a nonuniform axis ratio, which distorts the contour plots. - Algorithmic frameworks 17.1 (p. 494) and 17.2 (p. 505): need to choose new tolerance \tau_{k+1} in (0,\tau_k). - P. 497, l. 3: "quantities -c_i(x_k)/mu_k" (needs a minus sign). - P. 498: reference to eq. (17.10) should be to (17.9). - P. 511, l. 15: (by using (17.41d) and (17.41b)) -> (17.41c) as well? - P. 514, l. after eq. (17.47): "barrier parameter" -> penalty parameter. - P. 575, exercise 18.7: "...given in Exercise 3" -> Exercise 18.2? - P. 591 l. 9: if the sequences are nonnegative then there is no need for absolute values (eg in l. 12). - P. 618, ref. [140] Karmarkar: Combinatorics -> Combinatorica. - P. 619, ref. [157] Markowitz: volume 7, not 8.