Geodesic
Optimality conditions in the problem of maximization of the difference of two convex functions
Izvestiâ vysših učebnyh zavedenij. Matematika, no. 10 (2010), pp. 87-91.

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We consider a quadratic d. c. optimization problem on a convex set. The objective function is represented as the difference of two convex functions. By reducing the problem to the equivalent concave programming problem we prove a sufficient optimality condition in the form of an inequality for the directional derivative of the objective function at admissible points of the corresponding level surface.
Keywords: d. c.-maximization problem, necessary and sufficient optimality conditions. 
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     author = {N. S. Rozinova},
     title = {Optimality conditions in the problem of maximization of the difference of two convex functions},
     journal = {Izvesti\^a vys\v{s}ih u\v{c}ebnyh zavedenij. Matematika},
     pages = {87--91},
     publisher = {mathdoc},
     number = {10},
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     url = {http://geodesic.mathdoc.fr/item/IVM_2010_10_a10/}
}
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N. S. Rozinova. Optimality conditions in the problem of maximization of the difference of two convex functions. Izvestiâ vysših učebnyh zavedenij. Matematika, no. 10 (2010), pp. 87-91. http://geodesic.mathdoc.fr/item/IVM_2010_10_a10/

[1] Tuy H., “D. C. optimization: Theory, methods and algorithms”, Handbook of global optimization, v. 2, eds. Horst R., Pardalos P. M., Kluwer Academic Publishers, 1995, 149–216 | MR | Zbl

[2] Hiriart-Urruty J. B., “Conditions for global optimality”, Handbook of global optimization, v. 2, eds. Horst R., Pardalos P. M., Kluwer Academic Publishers, 1995, 1–26 | MR | Zbl

[3] Strekalovskii A. S., Elementy nevypukloi optimizatsii, Nauka, Novosibirsk, 2003

[4] Vasilev F. P., Metody optimizatsii, Faktorial Press, M., 2002