v2007.11.26 - Convex Optimization

31appendicesProvided so as to be more self-contained:linear algebra (appendix A is primarily concerned with properstatements of semidefiniteness for square matrices),simple matrices (dyad, doublet, elementary, Householder, Schoenberg,orthogonal, etcetera, in appendix B),a collection of known analytical solutions to some importantoptimization problems (appendix C),matrix calculus remains somewhat unsystematized when comparedto ordinary calculus (appendix D concerns matrix-valued functions,matrix differentiation and directional derivatives, Taylor series, andtables of first- and second-order gradients and matrix derivatives),an elaborate exposition offering insight into orthogonal andnonorthogonal projection on convex sets (the connection betweenprojection and positive semidefiniteness, for example, or betweenprojection and a linear objective function in appendix E),software in appendix F to discriminate EDMs, to determine conicindependence, to reduce or constrain rank of an optimal solution toa semidefinite program, and two distinct methods of reconstructing amap of the United States: one given only distance information, theother given only relative distance data (greater or less than).