Abstract
In Chapter 22, we studied a generalization of the linear programming problem in which variables were constrained to take on integer values. In this chapter, we consider a generalization of a different kind. Namely, we shall study the class of problems that would be linear programs except that the objective function is permitted to include terms involving products of pairs of variables. Such terms are called quadratic terms, and the problems we shall study are called quadratic programming problems.
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Notes
The portfolio optimization model presented in Section 23.1 was first introduced by Markowitz (1959). He received the 1990 Nobel Prize in Economics for this work.
Quadratic programming is the simplest class of problems from the subject called nonlinear programming. Two excellent recent texts that cover nonlinear programming are those by Bertsekas (1995) and Nash & Sofer (1996). The first paper that extended the path-following method to quadratic programming was Monteiro & Adler (1989). The presentation given here follows Vanderbei (1999).
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© 2001 Robert J. Vanderbei
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Vanderbei, R.J. (2001). Quadratic Programming. In: Linear Programming. International Series in Operations Research & Management Science, vol 37. Springer, Boston, MA. https://doi.org/10.1007/978-1-4757-5662-3_23
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DOI: https://doi.org/10.1007/978-1-4757-5662-3_23
Publisher Name: Springer, Boston, MA
Print ISBN: 978-1-4757-5664-7
Online ISBN: 978-1-4757-5662-3
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