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Quadratic Programming Models

In: Optimization for Decision Making

Author

Listed:
  • Katta G. Murty

    (University of Michigan
    King Fahd University of Petroleum and Minerals)

Abstract

Quadratic programming (QP) deals with a special class of mathematical programs in which a quadratic function of the decision variables is required to be optimized (i.e., either minimized or maximized) subject to linear equality and/or inequality constraints. Let x = (x 1, …, x n ) T denote the column vector of decision variables. In mathematical programming, it is standard practice to handle a problem requiring the maximization of a function f(x) subject to some constraints by minimizing − f(x) subject to the same constraints. Both problems have the same set of optimum solutions. Because of this, we restrict our discussion to minimization problems. A quadratic function of decision variables x is a function of the form $$Q(x) = \sum \limits _{i=1}^{n} \sum \limits _{j=i}^{n}{q}_{ ij}{x}_{i}{x}_{j}\ \ + \sum \limits _{j=1}^{n}{c}_{ j}{x}_{j}\ \ + {c}_{0}.$$

Suggested Citation

  • Katta G. Murty, 2010. "Quadratic Programming Models," International Series in Operations Research & Management Science, in: Optimization for Decision Making, chapter 0, pages 445-476, Springer.
    • Handle: RePEc:spr:isochp:978-1-4419-1291-6_9
    DOI: 10.1007/978-1-4419-1291-6_9
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