Geometry and Complexity

• M. Kojima and M. Yamashita.
  "Enclosing Ellipsoids and Elliptic Cylinders of Semialgebraic Sets and Their Application to Error Bounds in Polynomial Optimization",
  Research Report B-459, Department of Mathematical and Computing Science, Tokyo Institute of Technology, Meguro, Tokyo 152-8552, Japan, November 2009.
  opt-online
• I. Pólik and T. Terlaky.
  "On the computational complexity of gap-free duals for semidefinite programming",
  COR@L Technical Report, Lehigh University.
  opt-online
• H. Waki and M. Muramatsu.
  "Facial reduction algorithms for conic optimization problems",
  Technical Report CS-09-01, Department of Computer Science, The University of Electro-Communications, Tokyo, July 2009.
  opt-online
• L. Kong, L. Tuncel and N. Xiu.
  "Homogeneous Cone Complementarity Problems and $P$ Properties",
  Research Report, Department of Combinatorics and Optimization, University of Waterloo, Waterloo, Ontario, Canada, April 2009.
  opt-online
• L. Kong, L. Tuncel and N. Xiu.
  "Fischer-Burmeister Complementarity Function on Euclidean Jordan Algebras",
  Research Report CORR 2007-17, Department of Combinatorics and Optimization, University of Waterloo, Waterloo, Ontario, Canada, November 2007.
  opt-online
• J. W. Helton and J. Nie.
  "Sufficient and Necessary Conditions for Semidefinite Representability of Convex Hulls and Sets",
  Department of Mathematics, University of California San Diego, September 2007.
  opt-online
• Y. Zinchenko.
  "On hyperbolicity cones associated with elementary symmetric polynomials",
  McMaster University, Canada, 2007.
  opt-online
• O. Guler and . Gurtuna.
  "The extremal volume ellipsoids of convex bodies, their symmetry properties, and their determination in some special cases",
  Department of Mathematics and Statistics, University of Maryland, 2007.
  opt-online
• R. Hildebrand.
  "An LMI description for the cone of Lorentz-positive maps II",
  Laboratory Jean Kuntzmann (LJK), University Joseph Fourier, Grenoble, France, August 2007 .
  opt-online
• I. Polik and T. Terlaky.
  "Exact duality for optimization over symmetric cones",
  AdvOL Report 2007/10, Advanced Optimization Lab, McMaster University, Hamilton, ON, Canada, August 2007.
  opt-online
• B. Recht, M. Fazel and P. A. Parrilo.
  "Guaranteed Minimum-Rank Solutions of Linear Matrix Equations via Nuclear Norm Minimization",
  Technical Report, Center for the Mathematics of Information, California Institute of Technology, 2007.
  opt-online
• J. W. Helton and J. Nie.
  "Semidefinite Representation of Convex Sets",
  Department of Mathematics, University of California San Diego, 2007.
  opt-online
• L. Kong, L. Tuncel and N. Xiu..
  "Monotonicity of Löwner Operators and Its Applications to Symmetric Cone Complementarity Problems",
  Research Report, Department of Combinatorics and Optimization, University of Waterloo, 2007.
  opt-online
• A. Belloni and R. M. Freund.
  "A Geometric Analysis of Renegar's Condition Number, and its interplay with Conic Curvature",
  MIT Operations Research Center Working Paper OR-zzz-07.
  opt-online
• Z. X. Chan and D. Sun.
  "Constraint Nondegeneracy, Strong Regularity and Nonsingularity in Semidefinite Programming",
  Technical Report, Department of Mathematics, National University of Singapore, January 2007. .
  opt-online
• J. B. Lasserre.
  "Convex sets with lifted semidefinite representation",
  Technical report; LAAS-CNRS, Toulouse, France. December 2006.
  opt-online
• G. Pataki.
  "On the Closedness of the Linear Image of a Closed Convex Cone",
  University of North Carolina, December 2006.
  opt-online
• J. Nie, K. Ranestad, and B. Sturmfels.
  "The Algebraic Degree of Semidefinite Programming",
  University of California at Berkeley, November 2006. Revised January 2008.
  arxiv
• E. de Klerk.
  "The complexity of optimizing over a simplex, hypercube or sphere: a short survey",
  CentER Discussion paper 2006-85 Tilburg University, The Netherlands, September 2006 .
  opt-online
• L. Faybusovich.
  "Jordan-algebraic approach to convexity theorem for quadratic mappings",
  Research report, University of Notre Dame, June 2005.
  opt-online
• M. J. Todd.
  "Largest dual ellipsoids inscribed in dual cones ",
  Technical Report No. 1426, School of Operations Research and Industrial Engineering, Cornell University, June 2005.
  opt-online
• D. Sun.
  "The Strong Second-Order Sufficient Condition and Constraint Nondegeneracy in Nonlinear Semidefinite Programming and Their Implications",
  Technical Report, Department of Mathematics, National University of Singapore, Sinagpore, May 2005..
  opt-online
• D. Sun and J. Sun.
  "Lowner's Operator and Spectral Functions in Euclidean Jordan Algebras",
  Tech. Report, Dept. of Mathematics, National University of Singapore, Dec. 2004.
  opt-online
• L. Faybusovich.
  "Semidefinite descriptions of cones defining spectral mask constraints",
  Research Report, University of Notre Dame, March 2004.
  opt-online
• A. Shapiro and A. Nemirovski.
  "Duality of Linear Conic Problems",
  Preprint, School of Industrial and Systems Engineering, Georgia Institute of Technology, Atlanta, GA, 2003.
  opt-online
• Adrian Lewis.
  "The structured distance to ill-posedness for conic systems",
  Technical report, Simon Fraser University, 2003. Submitted to Mathematics of Operations Research.
  opt-online
• Gabor Pataki.
  "On the closedness of the linear image of a closed convex cone. Part I: necessary and sufficient conditions for nice cones, and core separation",
  Research Report TR-02-3, Department of Operations Research, University of North Carolina Chapel Hill, March 2003.
  opt-online
• J.-S. Pang, D. Sun, and J. Sun.
  "Semismooth Homeomorphisms and Strong Stability of Semidefinite and Lorentz Complementarity Problems",
  Department of Decision Sciences, National University of Singapore, Republic of Singapore 119260, April 2002.
  pdf-file (http)
• E. A. Yildirim. "On Sensitivity Analysis in Conic Programming",
  Preprint SUNYSB-AMS-01-20. Department of Applied Mathematics and Statistics, State University of New York, Stony Brook, NY 11794-3600, October 2001.
  optimization-online.
• Yu. E. Nesterov and M. J Todd. "On the Riemannian Geometry Defined by Self-Concordant Barriers and Interior-Point Methods", Technical Report No. 1290, School of Operations Research and Industrial Engineering, Cornell University, Ithaca, NY 14853-3801, August 2001.
  ps-file (ftp)
• M. Halicka , E. De Klerk and Cornelis Roos. "On the convergence of the central path in semidefinite optimization",
  Technical report, Faculty ITS, Delft University of Technology, Mekelweg 4, 2628 CD Delft, The Netherlands, June 2001.
  optimization-online, ps-file (http)
• R. M. Freund. "On the Primal-Dual Geometry of Level Sets in Linear and Conic Optimization",
  Working Paper, MIT Operations Research Center, August 2001.
  optimization-online
• J. F. Sturm and S. Zhang. "On cones of nonnegative quadratic functions",
  CentER Report 2001-26, Faculty of Economics, Tilburg University, May 2001.
  html-reference
• M. Epelman and R. M. Freund.
  "Pre-Conditioners and Relations between Different Measures of Conditioning for Conic Linear Systems",
  MIT Operations Research Center Working Paper OR344-00, July 2000.
  ps-file (http)
• A. Ben-Tal and A. Nemirovski.
  "On the quality of semidefinite approximations of uncertain semidefinite programs affected by box uncertainty",
  Research report #2/00, MINERVA Optimization Center, Technion - Israel Institute of Technology, Technion City, Haifa 32000, Israel, April 2000.
• G. Pataki.
  "A Simple Derivation of a Facial Reduction Algorithm, and Extended Dual Systems",
  Technical Report, Dept. of IE/OR, Columbia University, April 2000.
  ps.gz-file (http)
• R. M. Freund and J. R. Vera.
  "On the complexity of computing estimates of condition measures of a conic linear system",
  Technical Report 4/99, Dept. of Industrial and System Engineering, Catholic University of Chile, 1999.
  ps-file (http) or dvi-file (http)
• M. A. Nunez and R. M. Freund.
  "Condition-Measure Bounds on the Behavior of the Central Trajectory of a Semi-Definite Program",
  School of Business and Economics, Chapman University, One University Drive, Orange, CA 92866, August 1999.
  pdf-file (http)
• M. Kojima.
  "Moderate Nonlinearity = Convexity + Quadratic Concavity",
  Research Report B-348, Dept. of Mathematical and Computing Sciences, Tokyo Institute of Technology, Oh-Okayama, Meguro-ku, Tokyo 152-8852, Japan, March 1999.
  ps-file (http)
• A. S. Lewis.
  "Nonsmooth analysis of eigenvalues",
  Math. Program. 84: 1-24, January 1999.
  ps-file (http)
• Marina Epelman and Robert M. Freund.
  "Condition Number Complexity of an Elementary Algorithm for Computing a Reliable Solution of a Conic Linear System",
  Massachusetts Institute of Technology, December 1998.
  ps.Z-file (http) or dvi.Z-file (http)
• Y. Ye.
  "Approximating global quadratic optimization with convex quadratic constraints",
  Working Paper, Department of Management Sciences, The University of Iowa, July 1998.
  ps-file (ftp) or dvi-file (ftp)
• A. Nemirovski, K. Roos, and T. Terlaky.
  "On Maximization of Quadratic form over Intersection of Ellipsoids with Common Center",
  Report 98-26, Faculty of Technical Mathematics and Informatics, Delft University of Technology, June 1998.
  ps-file (http) or dvi-file (http)
• J. F. Sturm.
  "Error bounds for linear matrix inequalities",
  Mcmaster University, Canada, May 1998.
  ps-file (http)
• A. Forsgren.
  "Optimality conditions for nonconvex semidefinite programming",
  Technical Report TRITA-MAT-1998-OS6, Department of Mathematics, Royal Institute of Technology (KTH), May 1998.
  ps-file (http)
• J. F. Sturm and S. Zhang.
  "On sensitivity of central solutions in semidefinite programming",
  Econometric Institute Report 9813/A, Erasmus University, The Netherlands, March 1998.
  ps-file (http)
• L. Faybusovich.
  "Euclidean Jordan algebras and generalized affine-scaling vector fields",
  Research report, University of Notre Dame, January, 1998.
  ps-file (http)
• R. M. Freund and J. Vera.
  "Condition-Based Complexity of Convex Optimization in Conic Linear Form via the Ellipsoid Algorithm",
  September 1997.
  ps.Z-file (ftp) or dvi-file (ftp)
• J. Pena.
  "Computing the distance to infeasibility: theoretical and practical issues",
  October 1997.
  ps-file (http) or dvi-file (http)
• G. Pataki and L. Tuncel.
  "On the generic properties of convex optimization problems in conic form",
  Research Report 97-16, Department of Combinatorics and Optimization, University of Waterloo, Waterloo, Ontario, Canada, September 1997.
  ps-file (http)
• J. Pena.
  "Understanding the geometry of infeasible perturbations of a conic linear system",
  June 1997.
  ps-file (http) or dvi-file (http)
• Z.-Q. Luo, J.F. Sturm, and S. Zhang.
  "Duality Results for Conic Convex Porgramming",
  Report 9719/A, Econometric Institute EUR, P.O. Box 1738, 3000 DR, The Netherlands, April 1997.
  ps-file (http) or dvi.zip-file (http)
• L. Porkolab and L. Kachiyan.
  "On the Complexity of Semidefinite Programs",
  Journal of Global Optimization, Vol. 10, No. 4, 351-365, June 1997.
• G. Pataki.
  "Cone-LP's and Semidefinte Programs: Geometry and a Simplex-Type Method",
  IPCO V Proc., LNCS 1084, Springer 1996, pp.162-174.
  ps.gz-file (file)
• R. M. Freund and J. R. Vera,
  "Some Characterizations and Properties of the 'Distance to Ill-Posedness' and the Condition Measure of a Conic Linear System",
  October 1995.
  ps-file (http)
• A. S. Lewis.
  "Eigenvalue-constrained faces",
  Linear Algebra and Applications 269 (1998), 159-181.
  ps-file (http)
• O. Güler and L. Tuncel.
  "Chracterization of the barrier parameter of homogeneous convex cones",
  Mathematical Programming 81 (1998) 55-76.
• A. Shapiro.
  "First and Second Order Analysis of Nonlinear Semidefinite Programs",
  Mathematical Programming 77 (1997) 301-320.
  ps-file (http) or tex-file (http)
• A. Shapiro.
  "On Uniqueness of Lagrange Multipliers in Optimiazation Problems Subject to Cone Constraints",
  SIAM J. Optim., Vol. 7, No. 2, pp. 508-518, May 1997.
  ps-file (http) or tex-file (http)
• M. Ramana, L. Tuncel, and H. Wolkowicz.
  "Strong Duality for Semidefinite Porgramming",
  SIAM J. Optim., Vol. 7, No. 3, pp. 641-662, August 1997.
  ps.gz-file (ftp)
• F. Alizadeh, J.-P. A. Haeberly, and M. L. Overton.
  "Complementarity and nondegeneracy in semidefinite programming",
  Mathematical Programming 77 (1997) 111-128.
  ps.gz-file (file)
• M. Mesbahi, G. P. Papavassilopoulos.
  "A cone programming apporach to the bilinear matrix inequality problem and its geometry",
  Mathematical Programming 77 (1997) 247-272.
• M. Ramana.
  "An Exact Duality Theory for Semidefinite Programming and its Complexity Implications",
  Mathematical Programming 77 (1997) 129-162.
  ps.gz-file (ftp)
• M. Ramana and A. J. Goldman.
  "Some Geometric Results in Semidefinite Programming",
  Rutcor Research Report 37-94, October 1994.
  ps.gz-file (ftp)
• G. Pataki.
  "On the Rank of Extreme Matrices in Semidefinite Programs and the Multiplicity of Optimal Eigenvalues",
  Mathematics of Operations Research, Vol. 23, No. 2, pp. 339-358, May 1998.
  ps.gz-file (file)
• R. J. Vanderbei and B. Yang.
  "The simplest semidefinite programs are trivial",
  Mathematics of Operations Research, Vol. 20, No. 3, pp. 590-596, August 1995.
• R. D. Hill and S. R. Waters.
  "On the Cone of Positive Semidefinite Matrices",
  Linear Algebra and its Applications, 90:81-88, 1987.
• A. Shapiro.
  "Extremal problems on the set of nonnegative definite matrices",
  Linear Algebra and its Applications, 67:7-18, 1985.
• H. Wolkowicz.
  "Some applications of optimization in matrix theory",
  Linear Algebra and its Applications, 40:101-118, 1981.
• G. P. Barker and D. Carlson.
  "Cones of diagonally dominant matrices",
  Pacific Journal of Mathematics, Vol. 57, No. 1, pp. 15-32, 1975.