Hidden Convexity, Optimization, and Algorithms on Rotation Matrices
Published Online:1 Jul 2024https://doi.org/10.1287/moor.2023.0114
References
- [1] (2020) Non-unique games over compact groups and orientation estimation in cryo-EM. Inverse Problems 36(6):064002.Crossref, Google Scholar
- [2] (2002) A Course in Convexity, Graduate Studies in Mathematics, vol. 54 (American Mathematical Society, Providence, RI).Crossref, Google Scholar
- [3] (2016) Sums of squares and varieties of minimal degree. J. Amer. Math. Soc. 29(3):893–913.Crossref, Google Scholar
- [4] (1961) On the field of values of a matrix. Proc. Amer. Math. Soc. 12(1):61–66.Crossref, Google Scholar
- [5] (2022) On the tightness of semidefinite relaxations for rotation estimation. J. Math. Imaging Vision 64(1):57–67.Crossref, Google Scholar
- [6] (1983) Diagonal elements and eigenvalues of a real symmetric matrix. J. Math. Anal. Appl. 91(2):562–566.Crossref, Google Scholar
- [7] (2020) Active SLAM for mobile robots with area coverage and obstacle avoidance. IEEE/ASME Trans. Mechatronics 25(3):1182–1192.Crossref, Google Scholar
- [8] (2016) CVXPY: A Python-embedded modeling language for convex optimization. J. Machine Learn. Res. 17(1):2909–2913.Google Scholar
- [9] (1941) On the mapping of quadratic forms. Bull. Amer. Math. Soc. (N.S.) 47(6):494–498.Crossref, Google Scholar
- [10] Farrell JL, Stuelpnagel JC, Wessner RH, Velman JR, Brook JE (1966) A least squares estimate of satellite attitude (Grace Wahba). SIAM Rev. 8(3):384–386.Google Scholar
- [11] (2015) Obtaining a triangular matrix by independent row-column permutations. Elbassioni K, Makino K, eds. Algorithms and Computation (ISAAC 2015) (Springer, Berlin, Heidelberg), 165–175.Google Scholar
- [12] (2009) Suborthogonality and orthocentricity of matrices. Linear Algebra Appl. 430(1):296–307.Crossref, Google Scholar
- [13] (1979) The S-procedure and duality relations in nonconvex problems of quadratic programming. Vestn. LGU Ser. Mat. Mekh. Astron. 5(1):101–109.Google Scholar
- [14] (2022) A semidefinite relaxation for sums of heterogeneous quadratics on the Stiefel manifold. Preprint, submitted May 26, https://arxiv.org/abs/2205.13653v1.Google Scholar
- [15] (1981) The ellipsoid method and its consequences in combinatorial optimization. Combinatorica 1(2):169–197.Crossref, Google Scholar
- [16] (2012) Geometric Algorithms and Combinatorial Optimization, Algorithmics and Combinatorics, vol. 2 (Springer Science & Business Media, Berlin).Google Scholar
- [17] (2005) Convexity Properties of Hamiltonian Group Actions (American Mathematical Society, Providence, RI).Google Scholar
- [18] (2002) Algebraic Topology (Cambridge University Press, Cambridge, UK).Google Scholar
- [19] (1954) Doubly stochastic matrices and the diagonal of a rotation matrix. Amer. J. Math. 76(3):620–630.Crossref, Google Scholar
- [20] (2012) Matrix Analysis (Cambridge University Press, Cambridge, UK).Crossref, Google Scholar
- [21] (1975) On defining sets of vertices of the hypercube by linear inequalities. Discrete Math. 11(2):119–124.Crossref, Google Scholar
- [22] (1953) Sequential minimax search for a maximum. Proc. Amer. Math. Soc. 4(3):502–506.Crossref, Google Scholar
- [23] (2018) Compact Extended Linear Programming Models (Springer International Publishing, Cham, Switzerland), 113–121.Crossref, Google Scholar
- [24] (2011) Spacecraft reorientation in presence of attitude constraints via logarithmic barrier potentials. Proc. 2011 Amer. Control Conf. (IEEE, Piscataway, NJ), 450–455.Google Scholar
- [25] (2016) Point registration via efficient convex relaxation. ACM Trans. Graphics 35(4):1–12.Crossref, Google Scholar
- [26] (2012) Functional maps: A flexible representation of maps between shapes. ACM Trans. Graphics 31(4):1–11.Crossref, Google Scholar
- [27] (2007) A survey of the S-lemma. SIAM Rev. 49(3):371–418.Crossref, Google Scholar
- [28] (2015) Semidefinite descriptions of the convex hull of rotation matrices. SIAM J. Optim. 25(3):1314–1343.Crossref, Google Scholar
- [29] (2001) On the shape of numerical ranges associated with Lie groups. Taiwanese J. Math. 5(3):497–506.Crossref, Google Scholar
- [30] (2020) A survey of hidden convex optimization. J. Oper. Res. Soc. China 8(1):1–28.Crossref, Google Scholar

