\begin{thebibliography}{10} \bibitem{Heinz_Set} H.H. Bauschke and J.M. Borwein. \newblock On the convergence of von {N}eumann's alternating projection algorithm for two sets. \newblock {\em Set-Valued Anal.}, 1(2):185--212, 1993. \bibitem{BBJAT1} H.H. Bauschke and J.M. Borwein. \newblock Dykstra's alternating projection algorithm for two sets. \newblock {\em J. Approx. Theory}, 79(3):418--443, 1994. \bibitem{proj_surv} H.H. Bauschke and J.M. Borwein. \newblock On projection algorithms for solving convex feasibility problems. \newblock {\em SIAM Rev.}, 38(3):367--426, 1996. \bibitem{Berman} A.~Berman. \newblock {\em Cones, matrices and mathematical programming}. \newblock Springer-Verlag, Berlin-New York, 1973. \newblock Lecture Notes in Economics and Mathematical Systems, Vol. 79. \bibitem{gen_adrian} J.~Bolte, A.~Daniilidis, and A.S. Lewis. \newblock Generic optimality conditions for semialgebraic convex programs. \newblock {\em Math. Oper. Res.}, 36(1):55--70, 2011. \bibitem{BLY} J.~Borwein, G.~Li, and L.~Yao. \newblock Analysis of the convergence rate for the cyclic projection algorithm applied to basic semialgebraic convex sets. \newblock {\em SIAM Journal on Optimization}, 24(1):498--527, 2014. \bibitem{stab1} J.M. Borwein and W.B. Moors. \newblock Stability of closedness of convex cones under linear mappings. \newblock {\em J. Convex Anal.}, 16(3-4):699--705, 2009. \bibitem{stab} J.M. Borwein and W.B. Moors. \newblock Stability of closedness of convex cones under linear mappings {II}. \newblock {\em J. Nonlinear Anal. Optim.}, 1(1):1--7, 2010. \bibitem{face_henry} J.M. Borwein and H.~Wolkowicz. \newblock Facial reduction for a cone-convex programming problem. \newblock {\em J. Austral. Math. Soc. Ser. A}, 30(3):369--380, 1980/81. \bibitem{conv_alt} L.M. Bregman. \newblock The method of successive projection for finding a common point of convex sets. \newblock {\em Sov. Math. Dokl}, 6:688--692, 1965. \bibitem{vris} Y.-L. Cheung, S.~Schurr, and H.~Wolkowicz. \newblock Preprocessing and regularization for degenerate semidefinite programs. \newblock In {\em Computational and analytical mathematics}, volume~50 of {\em Springer Proc. Math. Stat.}, pages 251--303. Springer, New York, 2013. \bibitem{Coste-semi} M.~Coste. \newblock {\em An {I}ntroduction to {S}emialgebraic {G}eometry}. \newblock RAAG Notes, 78 pages, Institut de Recherche Math\'{e}matiques de Rennes, October 2002. \bibitem{prep} D.~Drusvyatskiy and A.S. Lewis. \newblock Generic nondegeneracy in convex optimization. \newblock {\em Proc. Amer. Math. Soc.}, 139(7):2519--2527, 2011. \bibitem{ext_ineq} D.~Drusvyatskiy, S.A. Vavasis, and H.~Wolkowicz. \newblock Extreme point inequalities and geometry of the rank sparsity ball. \newblock {\em arXiv:1401.4774}, 2014. \bibitem{GPR} L.G. Gubin, B.T. Polyak, and E.V. Raik. \newblock The method of projections for finding the common point of convex sets. \newblock {\em USSR Computational Mathematics and Mathematical Physics}, 7(6):1--24, 1967. \bibitem{homes} R.B. Holmes. \newblock {\em Geometric functional analysis and its applications}. \newblock Springer-Verlag, New York-Heidelberg, 1975. \newblock Graduate Texts in Mathematics, No. 24. \bibitem{gabor} G.~Pataki. \newblock Strong duality in conic linear programming: facial reduction and extended duals. \newblock In {\em Computational and analytical mathematics}, volume~50 of {\em Springer Proc. Math. Stat.}, pages 613--634. Springer, New York, 2013. \bibitem{gen_pat} G.~Pataki and L.~Tun{\c{c}}el. \newblock On the generic properties of convex optimization problems in conic form. \newblock {\em Math. Program.}, 89(3, Ser. A):449--457, 2001. \bibitem{con_ter} R.~T. Rockafellar. \newblock {\em Convex analysis}. \newblock Princeton Mathematical Series, No. 28. Princeton University Press, Princeton, N.J., 1970. \bibitem{sturm} J.F. Sturm. \newblock Error bounds for linear matrix inequalities. \newblock {\em SIAM J. Optim.}, 10(4):1228--1248 (electronic), 2000. \bibitem{N_proj} J.~von Neumann. \newblock {\em Functional {O}perators. {II}. {T}he {G}eometry of {O}rthogonal {S}paces}. \newblock Annals of Mathematics Studies, no. 22. Princeton University Press, Princeton, N. J., 1950. \bibitem{MW13} H.~Waki and M.~Muramatsu. \newblock Facial reduction algorithms for conic optimization problems. \newblock {\em J. Optim. Theory Appl.}, 158(1):188--215, 2013. \end{thebibliography}