Abstract
A novel technique is proposed to solve polynomial semi-definite programming problems. In particular, by coupling optimization techniques with algebraic geometry tools, it is shown how to determine closed-form solutions to this class of problems. The effectiveness of the proposed technique is validated via application to some optimum truss design problems involving constraints on the global stability of the structure and on the free vibration frequencies.
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References
C. Possieri, M. Sassano, Automatica 74, 23 (2016)
L. Menini, C. Possieri, A. Tornambe, IEEE Trans. Autom. Control 61(5), 1362 (2016)
D.A. Cox, J.B. Little, D. O’Shea, Using Algebraic Geometry (Springer, Berlin, 1998)
J.H. Van Lint, Introduction to Coding Theory, vol. 86 (Springer, New York, 2012)
D.E. Kirk, Optimal Control Theory: An Introduction (Courier Corporation, Honolulu, 2012)
Z. Szallasi, J. Stelling, V. Periwal, System Modeling in Cellular Biology (MIT Press, New York, 2006)
Y.S. Abu-Mostafa, M. Magdon-Ismail, H.T. Lin, Learning from Data (AMLBook, New York, 2012)
M. Kočvara, Struct. Multidiscip. Optim. 23(3), 189 (2002)
A. Wächter, L.T. Biegler, Math. Prog. 106(1), 25 (2006)
I.S. Duff, ACM Trans. Math. Soft. 30(2), 118 (2004)
D. Cox, J. Little, D. O’Shea, Ideals, Varieties, and Algorithms (Springer, Berlin, 2015)
B. Sturmfels, Solving Systems of Polynomial Equations (American Mathematical Society, Providence, 2002)
B.D.O. Anderson, R.W. Scott, Proc. IEEE 65(6), 849 (1977)
L. Menini, C. Possieri, A. Tornambe, Asian J. Control 20(2), 1 (2018)
K. Kurdyka, P. Orro, S. Simon, et al., J. Differ. Geom. 56(1), 67 (2000)
M.S. El Din, in International Symposium Symbolic Algebraic Computer (2008), pp. 71–78
F. Guo, M.S. El Din, L. Zhi, in International Symposium Symbolic Algebraic Computer (2010), pp. 107–114
Z. Jelonek, K. Kurdyka, Discrete Comput. Geom. 34(4), 659 (2005)
W. Karush, Minima of functions of several variables with inequalities as side conditions. Master’s thesis (University of Chicago, Chicago, 1939)
H.W. Kuhn, A.W. Tucker, in Proceedings Berkeley Symposium Mathematical Statistics and Probability (University California, Berkeley, 1951)
L. Menini, C. Possieri, A. Tornambe, IEEE Trans. Autom. Control 63(12), 4188 (2018)
C. Possieri, M. Sassano, in 54th IEEE Conference Decision Control (2015), pp. 5197–5202
C.-J. Thore, fminsdp (2021) (https://www.mathworks.com/matlabcentral/fileexchange/43643-fminsdp), MATLAB Central File Exchange. Retrieved September 24, 2021
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Menini, L., Possieri, C., Tornambe, A. (2022). An Algorithm to Determine the Exact Solution to Polynomial Semi-Definite Problems: Application to Structural Optimization. In: Lacarbonara, W., Balachandran, B., Leamy, M.J., Ma, J., Tenreiro Machado, J.A., Stepan, G. (eds) Advances in Nonlinear Dynamics. NODYCON Conference Proceedings Series. Springer, Cham. https://doi.org/10.1007/978-3-030-81162-4_52
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