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2 results

  • Lipschitz and differentiable dependence of solutions on a parameter in a scalarization method

  • Alicia Sterna-Karwat
  • Journal:
    Journal of the Australian Mathematical Society. Series A. Pure Mathematics and Statistics / Volume 42 / Issue 3 / June 1987
    Published online by Cambridge University Press:
    09 April 2009, pp. 353-364
    Print publication:
    June 1987
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  • This paper is concerned with a vector optimization problem set in a normed space where optimality is defined through a convex cone. The vector problem can be solved using a parametrized scalar problem. Under some convexity assumptions, it is shown that dependence of optimal solutions on the parameter is Lipschitz continuous. Hence differentiable dependence on the solutions on the parameter is derived.

  • A note on convex cones in topological vector spaces

  • Alicia Sterna-Karwat
  • Journal:
    Bulletin of the Australian Mathematical Society / Volume 35 / Issue 1 / February 1987
    Published online by Cambridge University Press:
    17 April 2009, pp. 97-109
    Print publication:
    February 1987
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  • The aim of the present note is an independent study of a class of convex cones, which is the largest possible with regard to existence of cone-maximal points in abstract vector optimization problems.