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Global Optimization of a Quadratic Functional with Quadratic Equality Constraints, Part 2

Author

Listed:
  • J. R. Bar-On

    (Hughes Missile Systems Company
    University of Oklahoma)

  • K. A. Grasse

    (University of Oklahoma)

Abstract

In this paper, we investigate a constrained optimization problem with a quadratic cost functional and two quadratic equality constraints. It is assumed that the cost functional is positive definite and that the constraints are both feasible and regular (but otherwise they are unrestricted quadratic functions). Thus, the existence of a global constrained minimum is assured. We develop a necessary and sufficient condition that completely characterizes the global minimum cost. Such a condition is of essential importance in iterative numerical methods for solving the constrained minimization problem, because it readily distinguishes between local minima and global minima and thus provides a stopping criterion for the computation. The result is similar to one obtained previously by the authors. In the previous result, we gave a characterization of the global minimum of a constrained quadratic minimization problem in which the cost functional was an arbitrary quadratic functional (as opposed to positive-definite here) and the constraints were at least positive-semidefinite quadratic functions (as opposed to essentially unrestricted here).

Suggested Citation

  • J. R. Bar-On & K. A. Grasse, 1997. "Global Optimization of a Quadratic Functional with Quadratic Equality Constraints, Part 2," Journal of Optimization Theory and Applications, Springer, vol. 93(3), pages 547-556, June.
    • Handle: RePEc:spr:joptap:v:93:y:1997:i:3:d:10.1023_a:1022691012894
    DOI: 10.1023/A:1022691012894
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    Cited by:

    1. S. M. Guu & Y. C. Liou, 1998. "On a Quadratic Optimization Problem with Equality Constraints," Journal of Optimization Theory and Applications, Springer, vol. 98(3), pages 733-741, September.
    2. J. B. Lasserre & J. B. Hiriart-Urruty, 2002. "Mathematical Properties of Optimization Problems Defined by Positively Homogeneous Functions," Journal of Optimization Theory and Applications, Springer, vol. 112(1), pages 31-52, January.

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