CONTINUITY OF THE OPTIMAL VALUE FUNCTION OF TWO-LEVEL PROGRAMMING
Abstract
Several problems of real life can be modeled as two-level mathematical programming problems. To solve these problems is not an easy work, it is frequent to use known methods of non-linear programming. For this it is necessary to formulate the two-level problem as one level problem. A good way to obtain this is using the well known optimal value function (or marginal function), for this reason it is convenient to known some of their more important proprieties. In this work we study the interest
in the solution two-level mathematical programming problem. At the end we show examples of two-level mathematical programming problem and we clarify some notions.
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References
Auslender A., Differentiable Stability in Nonconvex and Programming Study 10, pp 29-41, North - Holland, Amsterdam (1979).
Shimizu, K., Ishizuka Y., and Bard J., Non differentiable and Two – level mathematical programming, Kluwer Academic Plublishers, (1997).
Clarke F. , Optimization and Nonsmooth Analysis, John Wiley & Sons, New York (1983).
Gauvin J. and Dubeau F. , Differentiable Properties of the Marginal Study 19, pp 101-119, North Holland, Amsterdam (1979).
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