v2006.03.09 - Convex Optimization

44 CHAPTER 1. OVERVIEWEight appendices are provided 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 (appendix D concerns matrix-valued functions, theirderivatives and directional derivatives, Taylor series, and tables of firstandsecond-order gradients and derivatives),an elaborate and insightful exposition of orthogonal and nonorthogonalprojection on convex sets (the connection between projection andpositive semidefiniteness, for example, in appendix E),software to discriminate EDMs, conic independence, software to reducerank of an optimal solution to a semidefinite program, and two distinctmethods of reconstructing a map of the United States given onlydistance information (appendix G).