Conditions Characterizing Minima of the Difference of Functions |
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Authors: | Mirjam Dür |
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Institution: | (1) Vienna University of Economics and Business Administration, Austria, AT |
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Abstract: | Optimization problems involving differences of functions arouse interest as generalizations of so-called d.c. problems, i.e.
problems involving the difference of two convex functions. The class of d.c. functions is very rich, so d.c. problems are
rather general optimization problems. Several global optimality conditions for these d.c. problems have been proposed in the
optimization literature. We provide a survey of these conditions and try to detect their common basis. This enables us to
give generalizations of the conditions to situations when the objective function is no longer a difference of convex functions,
but the difference of two functions which are representable as the upper envelope of an arbitrary family of functions.
(Received 6 February 2001; in revised form 11 October 2001) |
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Keywords: | 2000 Mathematics Subject Classification: 90C26 90C46 |
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