v2007.09.13 - Convex Optimization

681dvector of distance-squared ijlower bound on distance-square d ijd ijABABCupper bound on distance-square d ijclosed line segment between points A and Bmatrix multiplication of A and Bclosure of set Cdecomposition orthonormal (1675) page 590, biorthogonal (1652) page 583expansion orthogonal (1685) page 592, biorthogonal (344) page 163vectorcubixquartixfeasible setsolution setnatural ordertightg ′g ′′→Ydgcolumn vector in R nmember of R M×N×Lmember of R M×N×L×Kmost simply, the set of all variable values satisfying all constraints ofan optimization problemmost simply, the set of all optimal solutions to an optimization problem;a subset of the feasible set and not necessarily a single pointwith reference to stacking columns in a vectorization means a vectormade from superposing column 1 on top of column 2 then superposingthe result on column 3 and so on; as in a vector made from entries of themain diagonal δ(A) means taken from left to right and top to bottomwith reference to a bound means a bound that can be met,with reference to an inequality means equality is achievablefirst derivative of possibly multidimensional function with respect toreal argumentsecond derivative with respect to real argumentfirst directional derivative of possibly multidimensional function g indirection Y ∈R K×L (maintains dimensions of g)