Abstract
In this chapter, we briefly review the results concerning the minimization of quadratic functions to the extent which is sufficient for understanding the algorithms described in Part II. The results are presented with specialized arguments, typically algebraic, that exploit the specific structure of these problems. Systematic exposition of optimization theory in the framework of nonlinear optimization can be found in the books by Bertsekas (Nonlinear Optimization, 1999, [1]), Nocedal and Wright (Numerical Optimization, 2000, [2]), Conn, Gould, and Toint (Trust Region Methods, 2000, [3]), Bazaraa, Sherali, and Shetty (Nonlinear Programming, Theory and Algorithms, 1993, [4]), or Griva, Nash, and Sofer (Linear and Nonlinear Optimization, 2009, [5]).
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References
Bertsekas, D.P.: Nonlinear Optimization. Athena Scientific, Belmont (1999)
Nocedal, J., Wright, S.F.: Numerical Optimization. Springer, New York (2000)
Conn, A.R., Gould, N.I.M., Toint, Ph.L: Trust Region Methods. SIAM, Philadelphia (2000)
Bazaraa, M.S., Shetty, C.M., Sherali, H.D.: Nonlinear Programming, Theory and Algorithms, 2nd edn. Wiley, New York (1993)
Griva, I., Nash, S.G., Sofer, A.: Linear and Nonlinear Optimization. SIAM, Philadelphia (2009)
Frank, M., Wolfe, P.: An algorithm for quadratic programming. Naval Research Logistic Quarterly 3, 95–110 (1956)
Dostál, Z.: On solvability of convex non-coercive quadratic programming problems. JOTA 143(2), 413–416 (2009)
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Dostál, Z. (2016). Optimization. In: Scalable Algorithms for Contact Problems. Advances in Mechanics and Mathematics, vol 36. Springer, New York, NY. https://doi.org/10.1007/978-1-4939-6834-3_3
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DOI: https://doi.org/10.1007/978-1-4939-6834-3_3
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