Typos/Inconsistencies/Comments/Additions

1. Page 4, Regarding comments on Lagrange and Lagrange multipliers: in

   author    = " B.H. POURCIAU",
   title     = "Modern multiplier methods",
   journal   = "American Mathematical Monthly",
   year      = "1980",
   volume    = "87",
   number    = "6",
   pages     = "433-451"}
   
   

   it is stated that Lagrange multipliers are actually due to Euler and that Lagrange was Euler's student.
2. Page 5, line 1: "underdetermined" should be replaced by: "usually underdetermined".
3. Page 8, line 20: "be the vector of unknown ..."
4. Page 13, last line: The matrix Q is symmetric and PSD means x'Qx >=0 for all x.
5. Page 20, Exercise 1.13: It is simpler if we change the notation slightly. Let Sⁿ be the vector space of n by n symmetric matrices and let Sⁿ₊ be the set of (symmetric) PSD matrices, i.e. the subscript + indicates PSD in the space of symmetric matrices. The inner product in this space is the trace inner product: (A,B)=trace AB.
6. Page 22, Definition 1.32: This is the definition of algebraic relative interior (sometimes called relative core). In finite dimension the relative core is equivalent to the topological relative interior. A better definition of x is a relative interior point of a convex set C is:
   
   • there exists an open ball of radius ε
   • with x in B_&epsilon(x);
   • B_&epsilon(x) intersect the affine hull of C is a subset of C.
7. Page 27, Definition 1.45: The limit should restrict &lambda > 0 in order to distinguish between the directions s and -s.
8. Page 30, Lemma 1.50: Hesse matrix refers to the Hessian matrix.
9. Page 45, Lemma 2.21: This Lemma is true without the assumption that (CO) is Slater regular.