Abstract
The material presented so far dealt largely with principles, methods, and algorithms for unconstrained optimization. In this and the next five chapters, we build on the introductory principles of constrained optimization discussed in Sects. 1.4–1.6 and proceed to examine the underlying theory and structure of some very sophisticated and efficient constrained optimization algorithms.
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Notes
- 1.
The rank of a matrix can also be found by using MATLAB command rank.
References
G. B. Dantzig, Linear Programming and Extensions. Princeton, NJ: Princeton University Press, 1963.
S. J. Wright, Primal-Dual Interior-Point Methods. Philadelphia, PA: SIAM, 1997.
S. Boyd, L. El Ghaoui, E. Feron, and V. Balakrishnan, Linear Matrix Inequalities in System and Control Theory. Philadelphia, PA: SIAM, 1994.
Y. Nesterov and A. Nemirovskii, Interior-Point Polynomial Algorithms in Convex Programming. Philadelphia, PA: SIAM, 1994.
J. T. Betts, “An accelerated multiplier method for nonlinear programming,” JOTA, vol. 21, no. 2, pp. 137–174, 1977.
G. Van der Hoek, “Reduction methods in nonlinear programming,” in Mathematical Centre Tracts, vol. 126. Amsterdam: Mathematisch Centrum, 1980.
R. Fletcher, Practical Methods of Optimization, 2nd ed. New York: Wiley, 1987.
G. H. Golub and C. F. Van Loan, Matrix Computations, 4th ed. Baltimore, MD: Johns Hopkins University Press, 2013.
A. Antoniou, Digital Signal Processing: Signals, Systems, and Filters. New York: McGraw-Hill, 2005.
W.-S. Lu, “A parameterization method for the design of IIR digital filters with prescribed stability margin,” in Proc. IEEE Int. Symp. Circuits and Systems, Hong Kong, Jun. 1997, pp. 2381–2384.
D. G. Luenberger and Y. Ye, Linear and Nonlinear Programming, 4th ed. New York: Springer, 2008.
E. K. P. Chong and S. H. Żak, An Introduction to Optimization. New York: Wiley, 1996.
W. Karush, “Minima of functions of several variables with inequalities as side constraints,” Master’s thesis, University of Chicago, Chicago, 1939.
H. W. Kuhn and A. W. Tucker, “Nonlinear programming,” in Proc. 2nd Berkeley Symposium, Berkeley, CA, 1951, pp. 481–492.
S. Boyd and L. Vandenberghe, Convex Optimization. Cambridge, UK: Cambridge University Press, 2004.
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Antoniou, A., Lu, WS. (2021). Fundamentals of Constrained Optimization. In: Practical Optimization. Texts in Computer Science. Springer, New York, NY. https://doi.org/10.1007/978-1-0716-0843-2_10
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