v2009.01.01 - Convex Optimization
v2009.01.01 - Convex Optimization v2009.01.01 - Convex Optimization
710 APPENDIX F. NOTATION AND A FEW DEFINITIONS [x i ] vector whose i th entry is x i x p particular value of x x 0 particular instance of x , or initial value of a sequence x i x 1 first entry of vector x , or first element of a set or list {x i } x ε extreme point x + vector x whose negative entries are replaced with 0 , or clipped vector x or nonnegative part of x ˇx x ⋆ x ∗ f ∗ P C x or Px P k x δ(A) δ 2 (A) δ(A) 2 λ i (X) λ(X) i λ(A) σ(A) Σ known data optimal value of variable x complex conjugate or dual variable or extreme direction of dual cone convex conjugate function projection of point x on set C , P is operator or idempotent matrix projection of point x on set C k or on range of implicit vector (A.1) vector made from the main diagonal of A if A is a matrix; otherwise, diagonal matrix made from vector A ≡ δ(δ(A)). For vector or diagonal matrix Λ , δ 2 (Λ) = Λ = δ(A)δ(A) where A is a vector i th entry of vector λ is function of X i th entry of vector-valued function of X vector of eigenvalues of matrix A , (1364) typically arranged in nonincreasing order vector of singular values of matrix A (always arranged in nonincreasing order), or support function diagonal matrix of singular values, not necessarily square
711 ∑ π(γ) Ξ Π ∏ ψ(Z) D D D T (X) D(X) T D −1 (X) D(X) −1 D ⋆ D ∗ sum nonlinear permutation operator (or presorting function) arranges vector γ into nonincreasing order (7.1.3) permutation matrix doublet or permutation matrix or operator product signum-like step function that returns a scalar for matrix argument (642), it returns a vector for vector argument (1465) symmetric hollow matrix of distance-square, or Euclidean distance matrix Euclidean distance matrix operator adjoint operator transpose of D(X) inverse operator inverse of D(X) optimal value of variable D dual to variable D D ◦ polar variable D ∂ partial derivative or matrix of distance-square squared (1290) or boundary of set K as in ∂K ∂y √ d ij d ij partial differential of y (absolute) distance scalar distance-square scalar, EDM entry V geometric centering operator, V(D)= −V DV 1 2
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- Page 673 and 674: E.8. RANGE/ROWSPACE INTERPRETATION
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- Page 705 and 706: Appendix F Notation and a few defin
- Page 707 and 708: 707 a.i. c.i. l.i. w.r.t affinely i
- Page 709: 709 is or ← → t → 0 + as in
- Page 713 and 714: 713 R m×n Euclidean vector space o
- Page 715 and 716: 715 H − H + ∂H ∂H ∂H −
- Page 717 and 718: 717 O O sort-index matrix order of
- Page 719 and 720: (x,y) angle between vectors x and y
- Page 721 and 722: Bibliography [1] Suliman Al-Homidan
- Page 723 and 724: BIBLIOGRAPHY 723 [24] Alexander I.
- Page 725 and 726: BIBLIOGRAPHY 725 [52] Stephen Boyd,
- Page 727 and 728: BIBLIOGRAPHY 727 [78] Frank Critchl
- Page 729 and 730: BIBLIOGRAPHY 729 [105] Richard L. D
- Page 731 and 732: BIBLIOGRAPHY 731 [132] Michel X. Go
- Page 733 and 734: BIBLIOGRAPHY 733 [162] T. Herrmann,
- Page 735 and 736: BIBLIOGRAPHY 735 [191] Mark Kahrs a
- Page 737 and 738: BIBLIOGRAPHY 737 [220] K. V. Mardia
- Page 739 and 740: BIBLIOGRAPHY 739 [250] Pythagoras P
- Page 741 and 742: BIBLIOGRAPHY 741 [277] Anthony Man-
- Page 743 and 744: BIBLIOGRAPHY 743 [306] Michael W. T
- Page 745 and 746: [333] Margaret H. Wright. The inter
- Page 747 and 748: Index 0-norm, 203, 261, 294, 296, 2
- Page 749 and 750: INDEX 749 product, 43, 92, 147, 254
- Page 751 and 752: INDEX 751 coordinates, 140, 170, 17
- Page 753 and 754: INDEX 753 affine dimension, 485 fea
- Page 755 and 756: INDEX 755 affine, 209 nonlinear, 19
- Page 757 and 758: INDEX 757 of point, 37 ray, 90 rela
- Page 759 and 760: INDEX 759 normal, 47, 548, 563 norm
711<br />
∑<br />
π(γ)<br />
Ξ<br />
Π<br />
∏<br />
ψ(Z)<br />
D<br />
D<br />
D T (X)<br />
D(X) T<br />
D −1 (X)<br />
D(X) −1<br />
D ⋆<br />
D ∗<br />
sum<br />
nonlinear permutation operator (or presorting function) arranges<br />
vector γ into nonincreasing order (7.1.3)<br />
permutation matrix<br />
doublet or permutation matrix or operator<br />
product<br />
signum-like step function that returns a scalar for matrix argument<br />
(642), it returns a vector for vector argument (1465)<br />
symmetric hollow matrix of distance-square,<br />
or Euclidean distance matrix<br />
Euclidean distance matrix operator<br />
adjoint operator<br />
transpose of D(X)<br />
inverse operator<br />
inverse of D(X)<br />
optimal value of variable D<br />
dual to variable D<br />
D ◦ polar variable D<br />
∂ partial derivative or matrix of distance-square squared (1290)<br />
or boundary of set K as in ∂K<br />
∂y<br />
√<br />
d ij<br />
d ij<br />
partial differential of y<br />
(absolute) distance scalar<br />
distance-square scalar, EDM entry<br />
V geometric centering operator, V(D)= −V DV 1 2
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