Errata for Linear and Nonlinear Programming by Stephen G. Nash and Ariela Sofer

Items are sorted by order of occurrence within the book. Negative line numbers are counted from the bottom of the page. Within displayed equations, matrices and vectors are counted as a single line. This file was last modifed on January 20, 1998.

Page xvii, line 6 change: http://bass.gmu.edu/site/ORE/Nash-Sofer.html to: http://www.gmu.edu/departments/ore/books/Nash-Sofer.html

Page 7, line 4

change: 2x_{2}

to: 2x_{1}

Page 20, line 17 change: g_{i}(x̂) > 0 if and only if to: if g_{i}(x̂) > 0 then

Page 20, line 19

change: defined by an equivalent set of equality and inequality constraints Ŝ in such a way that the

interior of Ŝ is empty.

to: represented by equality and inequality constraints in such a way that it has no interior points.

Page 35, line –10 change: (−2, 3) to: (−2, 3)^{T}

Page 37, line –4 change: be possible to: possible

Page 43, line –8 change: ∇f(x_{k})p to: ∇f(x_{k})^{T}p

Page 105, line –6 change: x_{1}, x_{2} ≥ 0 to: x_{1}, x_{2}, x_{3} ≥ 0

Page 133, line –7 change: surplus to: excess

Page 134, line 2,3 change: z_{∗} to: z′_{∗}

Page 165, line 14 change: more to: general Page 171, line –16

change: minimize to: maximize

Page 189, line 11 change: −2x_{1} − x_{2} to: −x_{1} − 2x_{2}

Page 207, line 7 change: ( 3 −5 −7 2 0 0 0 0 ) to: ( 3 −5 −7 2 0 0 0 0 )^{T}

Page 233, line 1 change: (1/â_{s,t}) to: (1/â_{s,t}^{2})

Page 244, line –15 change: to the dual of to: to

Page 259, line –1 (right-hand figure)

change: x_{1,5} = 0 to: x_{5,1} = 0

Also, reverse direction of arrow accordingly.

Page 259, line –1 (right-hand figure)

change: x_{4,7} = 0 to: x_{7,4} = 0

Also, reverse direction of arrow accordingly.

Page 270, line –9 change: 100^{i−j} to: 100^{i−1}

Page 296, line –4 change: x and x_{∗} to: x_{∗} and x_{∗} + p

Page 327, line 13 change: 10^{−2} to: 10^{−7}

Page 341, line 10 change: Problem 1 to: Problem 3

Page 347, line –12 change: maximization to: minimization

Page 357, line 10 change: s_{1}, …, s_{n} to: s_{0}, …, s_{n−1} Page 357, line 11

change: 0, 2, to: 0, 1,

Page 357, line 17 change: v is some nonzero vector. to: v is a vector such that v^{T}s_{k} ≠ 0.

Page 361, line –8 change: +\frac{1}{12} to: – \frac{1}{12}

Page 361, line –3 change: +\frac{1}{24} to: – \frac{1}{24}

Page 395, line –5 change: methods to: method

Page 401, line 4 change: entire line to:

\begin{aligned}H_{k} & = & H_{k−1} − \frac{s_{k−1}(H_{k−1}y_{k−1})^{T}(H_{k−1}y_{k−1})s_{k−1}^{T}}{y_{k−1}^{T}s_{k−1}} + \frac{y_{k−1}^{T}s_{k−1}+y_{k−1}^{T}H_{k−1}y_{k−1}}{(y_{k−1}^{T}s_{k−1})^{2}} (s_{k−1}^{T}s_{k−1}) \\ & = & [I − \frac{s_{k−1}y_{k−1}^{T}}{y_{k−1}^{T}s_{k−1}}] H_{k−1} [I − \frac{y_{k−1}s_{k−1}^{T}}{y_{k−1}^{T}s_{k−1}}] + \frac{s_{k−1}s_{k−1}^{T}}{y_{k−1}^{T}s_{k−1}} \end{aligned}

Page 401, line 10–13 change: entire displayed formula to:

p_{k} = −H_{k}∇f(x_{k}) = − [I − \frac{s_{k−1}y_{k−1}^{T}}{y_{k−1}^{T}s_{k−1}}] [I − \frac{y_{k−1}s_{k−1}^{T}}{y_{k−1}^{T}s_{k−1}}] ∇f(x_{k}) − \frac{s_{k−1}s_{k−1}^{T}}{y_{k−1}^{T}s_{k−1}}∇f(x_{k})

Page 407, line 6 change: r_{i}^{T}Mr_{j} = 0, r_{i}^{T}Mp_{j} = 0, and p_{i}^{T}Ar_{j} = 0 to: r_{i}^{T}M^{−1}r_{j} = 0, r_{i}^{T}p_{j} = 0, and p_{i}^{T}M^{1/2}AM^{1/2}r_{j} = 0

Page 438, line –3 change: increase to: decrease

Page 442, line –14 change: λ

to:  λ̂_{∗}

Page 450, line 3 change: (2x_{1}, 4x_{2})^{T} = (2, 0)^{T} to: (2x_{1}, 4x_{2})^{T} = (4, 0)^{T}

Page 468, line 17 change: Lemma 14.5 to: Lemma 14.7 Page 470, line –12

change: min_{x} x^{2} − λ(x − 1)

to:  min_{x}{x^{2} − λ(x − 1)}

Page 479, line –3 change: AQ^{−1}Ac to: AQ^{−1}c

Page 480, line 5 change: log(x) to: e^{x}

Page 510, line –15 change: project to: projection

Page 553, line –7 change: is minimizes to: minimizes

Page 561, line –6 change: f(x) + λ^{T}g(x) to: f(x) − λ^{T}g(x)

Page 574, line –9 change: A_{y}^{T} to: A^{T}y

Page 589, line 10 change: (P̄) to: (P K)

Page 589, line 11

change: P̄

to: (P K)

Page 591, line 4

change: P̄

to: (P K)

Page 591, line 5

change: P̄

to: (P K)

Page 608, line –13 change: function of t to: function of ρ

Page 613, line 1 change: call to: called