Some new Farkas-type results for inequality systems with DC functions
- First Online:
We present some Farkas-type results for inequality systems involving finitely many DC functions. To this end we use the so-called Fenchel-Lagrange duality approach applied to an optimization problem with DC objective function and DC inequality constraints. Some recently obtained Farkas-type results are rediscovered as special cases of our main result.
KeywordsFarkas-type results DC functions Conjugate duality
Unable to display preview. Download preview PDF.
- 2.Boţ R.I. and Wanka G. (2005). Duality for multiobjective optimization problems with convex objective functions and D.C. constraints. J. Math. Anal. Appl. 315: 526–543 Google Scholar
- 4.Boţ, R.I., Wanka, G.: Farkas-type results for max-functions and applications. Positivity. 10(4):761–777Google Scholar
- 14.Pham D.T. and El Bernoussi S. (1988). Duality in d. c. (difference of convex functions) optimization. Subgradient methods. Int. Ser. Numerical Math. 84: 277–293 Google Scholar
- 15.Rockafellar R.T. (1970). Convex Analysis. Princeton University Press, Princeton Google Scholar
- 16.Rubinov A.M., Glover B.M. and Jeyakumar V. (1995). A general approach to dual characterizations of solvability of inequality systems with applications. J. Convex Anal. 2: 309–344 Google Scholar
- 17.Tuy H. (1987). Global minimization of a difference of two convex functions. Math. Program. Study 30: 150–182 Google Scholar
- 18.Tuy H. (1995). D.C. optimization: theory, methods and algorithms. Nonconvex Optimization Appl. 2: 149–216 Google Scholar
- 21.Wanka, G., Boţ, R.I.: On the relations between different dual problems in convex mathematical programming. In: Chamoni, P., Leisten, R., Martin, A., Minnermann, J., Stadtler, H. (eds.) Operations Research Proceedings 2001. Springer Verlag, Berlin (2002)Google Scholar