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Mond–Weir duality

In: Optimization

Author

Listed:
  • B. Mond

    (La Trobe University
    University of Melbourne)

Abstract

Consider the nonlinear programming problem to minimize $$f(x)$$ subject to $$g(x) \leq 0$$ . The initial dual to this problem given by Wolfe required that all the functions be convex. Since that time there have been many extensions that allowed the weakening of the convexity conditions. These generalizations include pseudo- and quasi-convexity, invexity, and second order convexity. Another approach is that of Mond and Weir who modified the dual problem so as to weaken the convexity requirements. Here we summarize and compare some of these different approaches. It will also be pointed out how the two different dual problems (those of Wolfe and Mond–Weir) can be combined. Some applications, particularly to fractional programming, will be discussed.

Suggested Citation

  • B. Mond, 2009. "Mond–Weir duality," Springer Optimization and Its Applications, in: Charles Pearce & Emma Hunt (ed.), Optimization, edition 1, chapter 0, pages 157-165, Springer.
    • Handle: RePEc:spr:spochp:978-0-387-98096-6_8
    DOI: 10.1007/978-0-387-98096-6_8
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