Lifts of Convex Sets and Cone Factorizations
Published Online:18 Jan 2013https://doi.org/10.1287/moor.1120.0575
References
- . Disjunctive programming. Ann. Discrete Math. (1979) 5:3–51Crossref, Google Scholar
- . A Course in Convexity, Graduate Studies in Mathematics (2002) 54(American Mathematical Society, Providence, RI) Google Scholar
- . Approximations of convex bodies by polytopes and by projections of spectrahedra. (2012) . ArXiv:1204.0471Google Scholar
- . Extreme copositive quadratic forms. Acta Arithmetica (1969) XV:319–327Google Scholar
- . Lectures on Modern Convex Optimization (2001) (Society for Industrial and Applied Mathematics (SIAM), Philadelphia) MPS/SIAM Series on OptimizationCrossref, Google Scholar
- . On polyhedral approximations of the second-order cone. Math. Oper. Res. (2001) 26(2):193–205Link, Google Scholar
- . Subset algebra lift operators for 0-1 integer programming. SIAM J. Optim. (2004) 15(1):63–95Crossref, Google Scholar
- . Regularizing the abstract convex program. J. Math. Anal. Appl. (1981) 83(2):495–530Crossref, Google Scholar
- . On the copositive representation of binary and continuous nonconvex quadratic programs. Math. Programming (2009) 120(2, Ser. A):479–495Crossref, Google Scholar
- . Nonnegative ranks, decompositions, and factorizations of nonnegative matrices. Linear Algebra Appl. (1993) 190:149–168Crossref, Google Scholar
- . Combinatorial bounds on nonnegative rank and extended formulations. Discrete Math. (2013) 313(1):67–83Crossref, Google Scholar
- . Linear vs. semidefinite extended formulations: Exponential separation and strong lower bounds. Proc. 44th Sympos. Theory Comput., STOC '12 (2012) (ACM, New York) 95–106Crossref, Google Scholar
- . On the geometric interpretation of the nonnegative rank. Linear Algebra Appl. (2012) 437(11):2685–2712Crossref, Google Scholar
- . Smallest compact formulation for the permutahedron. (2009) . http://www-math.mit.edu/∼goemans/publ.htmlGoogle Scholar
- . Theta bodies for polynomial ideals. SIAM J. Optim. (2010) 20(4):2097–2118Crossref, Google Scholar
- . Polytopes of minimum positive semidefinite rank. (2012) . ArXiv:1205.5306Google Scholar
- . Symmetry matters for the sizes of extended formulations. Integer Programming and Combinatorial Optimization (2010) 6080(Springer, Berlin) 135–148Lecture Notes in Computer ScienceCrossref, Google Scholar
- . Cones of matrices and successive convex relaxations of nonconvex sets. SIAM J. Optim. (2000) 10(3):750–778Crossref, Google Scholar
- . Global optimization with polynomials and the problem of moments. SIAM J. Optim. (2001) 11(3):796–817Crossref, Google Scholar
- . Cones of matrices and set-functions and 0-1 optimization. SIAM J. Optim. (1991) 1(2):166–190Crossref, Google Scholar
- . Positive Polynomials and Sums of Squares, Mathematical Surveys and Monographs (2008) 146(American Mathematical Society, Providence, RI) Google Scholar
- . Interior Point Polynomial Methods in Convex Programming, Studies in Applied Mathematics (1994) 13(SIAM, Philadelphia) Crossref, Google Scholar
- . Semidefinite programming relaxations for semialgebraic problems. Math. Programming (2003) 96(2, Ser. B):293–320Crossref, Google Scholar
- . Symmetry in extended formulations of the permutahedron. (2009) . ArXiv:0912.3446Google Scholar
- . On the connection of facially exposed, and nice cones. J. Math. Analysis and Applications (2013) 400(1):211–221Crossref, Google Scholar
- . On the computational complexity and geometry of the first-order theory of the reals. I. Introduction. Preliminaries. The geometry of semi-algebraic sets. The decision problem for the existential theory of the reals. J. Symbolic Comput. (1992) 13(3):255–299Crossref, Google Scholar
- . Hyperbolic programs, and their derivative relaxations. Foundations Comput. Math. (2006) 6(1):59–79Crossref, Google Scholar
- . A hierarchy of relaxations between the continuous and convex hull representations for zero-one programming problems. SIAM J. Discrete Math. (1990) 3(3):411–430Crossref, Google Scholar
- . On the complexity of nonnegative matrix factorization. SIAM J. Optim. (2009) 20(3):1364–1377Crossref, Google Scholar
- . Expressing combinatorial optimization problems by linear programs. J. Comput. System Sci. (1991) 43(3):441–466Crossref, Google Scholar

