A general alternative theorem for convexlike functions is given. This permits the establishment of optimality conditions for convexlike programming problems in which both inequality and equality constraints are considered. It is shown that the main results of the paper contain, in particular, those of Craven, Giannessi, Jeyakumar, Hayashi, and Komiya, Simons, Zalinescu, and a recent result of Tamminen.
- convexlike functions
- constrained optimization problems
- duality theory
- alternative theorems of Farkas type
Illes, T., & Kassay, G. (1999). Theorems of the alternative and optimality conditions for convexlike and general convexlike programming. Journal of Optimization Theory and Applications, 101(2), 243-257. https://doi.org/10.1023/A:1021781308794