Abstract
Necessary and sufficient optimality conditions of the difference of convex functions are derived for unconstrained optimization problems. Connection between extremal properties of the difference of convex functions and the extremal properties of the difference of their conjugate functions is established. Duality theorems are proved. A smooth approximation of a d.c. function is investigated.
The research was supported by the Russian Foundation for Fundamental Studies (grant RFFI No. 97-01-00499)
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References
Rockafellar R.T.(1970). Convex Analysis. Princeton University Press.
Polyakova L.N.(1980). Necessary conditions for an extremum of quasidifferentiable functions, Vestnik of Leningrad Univ., 13, 57–62.
Hiriart-Urruty J.-B. (1985). Generalised differentiability, duality and optimization for problems dealing with differences of convex functions. In: Convexity and duality in Optimizaion, Ed. J. Ponstein, 37–50, Lecture Notes in Economics and Мathematical Systems. Vol.256, Springer.
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© 2001 Kluwer Academic Publishers
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Polyakova, L.N. (2001). On Global Properties of D.C.Functions. In: Gilbert, R.P., Panagiotopoulos, P.D., Pardalos, P.M. (eds) From Convexity to Nonconvexity. Nonconvex Optimization and Its Applications, vol 55. Springer, Boston, MA. https://doi.org/10.1007/978-1-4613-0287-2_16
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DOI: https://doi.org/10.1007/978-1-4613-0287-2_16
Publisher Name: Springer, Boston, MA
Print ISBN: 978-1-4613-7979-9
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