Corrections for the book NONLINEAR PROGRAMMING: 2ND
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p. 16 (-6) Change x < 2π to y < 2π p. 21 (+4) Change 4π 3 to 5π 6 p. 43 The following is a more streamlined proof of Prop. 1.2.1 (it eliminates the vector pk). The modifications begin at the 8th line of p. 44, where pk is introduced, but the proof is given here in its entirety for completeness. Proof: Consider the Armijo rule, and to arrive at a contradiction, assume that x is a limit point of {xk} with ∇f(x) 6= 0. Note that since {f(xk)} is monotonically nonincreasing, {f(xk)} either converges to a finite value or diverges to −∞. Since f is continuous, f(x) is a limit point of {f(xk)}, so it follows that the entire sequence {f(xk)} converges to f(x). Hence, f(xk)− f(xk+1) → 0.