Semidefinite Relaxations for Lebesgue and Gaussian Measures of Unions of Basic Semialgebraic Sets
Published Online:18 Sep 2019https://doi.org/10.1287/moor.2018.0980
References
- [1] (2012) Handbook of Semidefinite, Conic and Polynomial Optimization. International Series in Operations Research & Management Science (Springer, New York).Crossref, Google Scholar
- [2] (1997) Volume estimates and rapid mixing. Flavors of Geometry, vol. 31 (Cambridge University Press, Cambridge, UK), 151–180.Google Scholar
- [3] (2014) A cubic algorithm for computing Gaussian volume. Proc. ACM-SIAM Sympo. Discrete Algorithms (SODAlf) (SIAM, Philadelphia).Crossref, Google Scholar
- [4] (2016) A practical volume algorithm. Math. Programming Comput. 8(2):133–160.Crossref, Google Scholar
- [5] (2017) Simple approximations of semialgebraic sets and their applications to control. Automatisa 78:110–118.Crossref, Google Scholar
- [6] (1958) Linear Operators. Part I: General Theory (John Wiley & Sons, New York).Google Scholar
- [7] (1988) The complexity of computing the volume of a polyhedron. SIAM J. Comput. 17(5):967–974.Crossref, Google Scholar
- [8] (1991) A random polynomial-time algorithm for approximating the volume of convex bodies. J. ACM 38(1):1–17.Crossref, Google Scholar
- [9] (2009) GloptiPoly 3: Moments, optimization and semidefinite programming. Optim. Methods Softwares 24(4–5):761–779.Crossref, Google Scholar
- [10] (2009) Approximate volume and integration for basic semialgebraic sets. SIAM Rev. 51(4):722–743.Crossref, Google Scholar
- [11] (2010) Moments, Positive Polynomials and Their Applications (Imperial College Press, London).Google Scholar
- [12] (2011) A new look at nonnegativity on closed sets and polynomial optimization. SIAM J. Optim. 21(3):864–885.Crossref, Google Scholar
- [13] (2017) Computing Gaussian and exponential measures of semi-algebraic sets. Adv. Appl. Math. 91:137–163.Crossref, Google Scholar
- [14] (1992) Random Number Generation and Quasi-Monte Carlo Methods (SIAM, Philadelphia).Crossref, Google Scholar
- [15] (1993) Positive polynomials on compact semi-algebraic sets. Indiana Univ. Math. J. 42(3):969–984.Crossref, Google Scholar
- [16] (2005) Strong duality conditions in semidefinite programming. J. Electr. Engrg. 56(12):1–5.Google Scholar

