Concepts and techniques of optimization on the sphere
Tóm tắt
Từ khóa
Tài liệu tham khảo
Afsarii B, Tron R, René R (2013) On the convergence of gradient descent for finding the Riemannian center of mass. SIAM J Control Optim 51(3):2230–2260
Barani A, Pouryayevali MR (2009) Invariant monotone vector fields on Riemannian manifolds. Nonlin Anal 70(5):1850–1861
Dahl G, Leinaas JM, Myrheim J, Ovrum E (2007) A tensor product matrix approximation problem in quantum physics. Linear Algebra Appl 420(2–3):711–725
Das P, Chakraborti NR, Chaudhuri PK (2001) Spherical minimax location problem. Comput Optim Appl 18(3):311–326
Dennis JE, Jr, Schnabel RB (1996) Numerical methods for unconstrained optimization and nonlinear equations, vol 16 of Classics in Applied Mathematics. Society for Industrial and Applied Mathematics (SIAM), Philadelphia
do Carmo MP (1976) Differential geometry of curves and surfaces. Prentice-Hall Inc, Englewood Cliffs (Translated from the Portuguese)
do Carmo MP (1992) Riemannian geometry. Mathematics: theory and applications. Birkhäuser Boston Inc, Boston (Translated from the second Portuguese edition by Francis Flaherty)
Drezner Z, Wesolowsky GO (1983) Minimax and maximin facility location problems on a sphere. Naval Res Logist Quart 30(2):305–312
Ferreira OP, Iusem AN, Nemeth SZ (2013) Projections onto convex sets on the sphere. J Glob Optim 57:663–676
Ferreira OP, Oliveira P (1998) Subgradient algorithm on Riemannian manifolds. J Optim Theory Appl 97(1):93–104
Ferreira R, Xavier J, Costeira J, Barroso V (2008) Newton algorithms for riemannian distance related problems on connected locally symmetric manifolds. Thechnical Report: Institute for Systems and Robotics (ISR), Signal and Image Processing Group (SPIG), Instituto Superior Tecnico (IST)
Fletcher PT, Venkatasubramanian S, Joshi S (2009) The geometric median on Riemannian manifolds with application to robust atlas estimation. NeuroImage 45:S143–S152
Han D, Dai HH, Qi L (2009) Conditions for strong ellipticity of anisotropic elastic materials. J Elast 97(1):1–13
He S, Li Z, Zhang S (2010) Approximation algorithms for homogeneous polynomial optimization with quadratic constraints. Math Program 125(2):353–383
Iqbal A, Ali S, Ahmad I (2012) On geodesic E-convex sets, geodesic E-convex functions and E-epigraphs. J Optim Theory Appl 155(1):239–251
Iusem A, Seeger A (2005) On pairs of vectors achieving the maximal angle of a convex cone. Math Program 104(2—-3):501–523
Laurent M (2009) Sums of squares, moment matrices and optimization over polynomials. In: Putinar M, Sullivant S (eds) Emerging applications of algebraic geometry, vol 149 of IMA Vol. Math. Appl. Springer, New York, pp 157–270
Li C, Yao J-C (2012) Variational inequalities for set-valued vector fields on Riemannian manifolds: convexity of the solution set and the proximal point algorithm. SIAM J Control Optim 50(4):2486–2514
Li S-L, Li C, Liou Y-C, Yao J-C (2009) Existence of solutions for variational inequalities on Riemannian manifolds. Nonlinear Anal 71(11):5695–5706
Ling C, Nie J, Qi L, Ye Y (2009) Biquadratic optimization over unit spheres and semidefinite programming relaxations. SIAM J Optim 20(3):1286–1310
Qi L, Teo KL (2003) Multivariate polynomial minimization and its application in signal processing. J Glob Optim 26(4):419–433
Qi L, Wang F, Wang Y (2009) $$Z$$ Z -eigenvalue methods for a global polynomial optimization problem. Math Program 118(2):301–316
Reznick B (2000) Some concrete aspects of Hilbert’s 17th Problem. In: Real algebraic geometry and ordered structures (Baton Rouge, LA, 1996), vol 253 of Contemp. Math. Amer. Math. Soc., Providence, pp 251–272
Sakai T (1996) Riemannian geometry, volume 149 of Translations of Mathematical Monographs. American Mathematical Society, Providence (Translated from the 1992 Japanese original by the author)
Smith ST (1994) Optimization techniques on Riemannian manifolds. In: Hamiltonian and gradient flows, algorithms and control, vol 3 of Fields Inst. Commun. Amer. Math. Soc., Providence, pp 113–136
So AMC (2011) Deterministic approximation algorithms for sphere constrained homogeneous polynomial optimization problems. Math Program 129(2):357–382
Weiland S, van Belzen F (2010) Singular value decompositions and low rank approximations of tensors. IEEE Trans Signal Process 58(3):1171–1182
Xue G-L (1994) A globally convergent algorithm for facility location on a sphere. Comput Math Appl 27(6):37–50
Xue GL (1995) On an open problem in spherical facility location. Numer Algorithms 9(1–2):1–12
Zhang L (2003) On the convergence of a modified algorithm for the spherical facility location problem. Oper Res Lett 31(2):161–166