Abstract
We obtain rigorous estimates for linear and semidefinite relaxations of global optimization problems on the simplex and on the sphere
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References
Ben-Tal A., Nemirovski A. (2001),“ Lectures on Modern Convex Optimization,”, SIAM,pp.1–488.
Faybusovich L. (2002), “ On Nesterov’s approach to semi-infinite programming,” Acta Applicandae Mathematicae, vol. 74, pp. 195–215.
Reznick B. (1992),“ Sums of even powers of real linear forms,”Memoirs of AMS, vol. 96, no. 463,pp. 1–155.
Reznick B. (1995), “Uniform denominators in Hilbert’s seventeenth problem,” Math. Z.,vol.220, no. 1, pp. 75–97.
Powers V., Reznick B. (2001) “ A new bound for Po lya’s theorem with applications to polynomials positive on polyhedra,” J. Pure Appl. Algebra 164, 164, no. 1–2,pp. 221–229.
Nesterov Yu., Nemirovskii A. “Interior-point polynomial algorithms in convex programming,” SIAM Studies in Applied Mathematics, vol. 13. Society for Industrial and Applied Mathematics (SIAM), Philadelphia, PA, 1994. pp 405.
Bomze M., De Klerk E. (2002) “ Solving standard quadratic optimization problems via linear, semidefinite and copositive programming,” J. Global Optim.,vol. 24, no. 2, pp. 163–185.
Lasserre J. (2000/01) “Global optimization with polynomials and the problem of moments,” SIAM J. Optim.,vol. 11, no. 3, pp. 796–817 (electronic).
Nesterov Y. (1999) “Global quadratic optimization on the sets with simplex structure,” Discussion paper 9915, CORE, Katholic University of Louvain,Belgium.
Natanson M. (1996) “Additive Number Theory,” Springer Verlag pp. 1–342.
Pardalos P.M., Resende M.G.C. (1996) “Interior Point Methods for Global Optimization Problems”. In Interior Point methods of Mathematical Programming, T. Terlaky ed., Kluwer Academic Publishers, pp. 467–500.
Mitchell J., Pardalos P. M., and Resende M.G.C.(1998) “Interior Point Methods for Combinatorial Optimization”. In Handbook of Combinatorial Optimization Vol. 1 (D.-Z Du and P. Pardalos, editors), pp. 189–298.
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Faybusovich, L. (2004). Global Optimization of Homogeneous Polynomials on the Simplex and on the Sphere. In: Floudas, C.A., Pardalos, P. (eds) Frontiers in Global Optimization. Nonconvex Optimization and Its Applications, vol 74. Springer, Boston, MA. https://doi.org/10.1007/978-1-4613-0251-3_6
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DOI: https://doi.org/10.1007/978-1-4613-0251-3_6
Publisher Name: Springer, Boston, MA
Print ISBN: 978-1-4613-7961-4
Online ISBN: 978-1-4613-0251-3
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