v2010.10.26 - Convex Optimization

784 APPENDIX F. NOTATION AND A FEW DEFINITIONSarg inf f(x)argument x at infimum of function f ; not necessarily unique or amember of function domainiff if and only if , necessary and sufficient; also the meaningindiscriminately attached to appearance of the word “if ” in thestatement of a mathematical definition, [128, p.106] [258, p.4] anesoteric practice worthy of abolition because of ambiguity thusconferredrelintlimsgnroundmodtrrankrelativeinteriorlimitsignum function or signround to nearest integermodulus functionmatrix traceas in rankA, rank of matrix A ; dim R(A)dim dimension, dim R n = n , dim(x∈ R n ) = n , dim R(x∈ R n ) = 1,dim R(A∈ R m×n )= rank(A)affdim affaffine hullaffine dimensioncard cardinality, number of nonzero entries cardx ‖x‖ 0or N is cardinality of list X ∈ R n×N (p.323)convconecenvcontentconvex hull (2.3.2)conic hull (2.3.3)convex envelope (7.2.2.1)of high-dimensional bounded polyhedron, volume in 3 dimensions, areain 2, and so on