Symmetric duality with pseudo-invexity in variational problems
In 1961, Wolfe, in his pioneering research work, has presented a duality theorem for the theory of nonlinear mathematical programming, by introducing a new variable corresponding to primal constants, for the formation of a dual. It is to be emphasized that the primal can not be obtained by forming the dual of the dual, except in linear programs; but Dantzig, Esenberg, Cottle (1965) and Dorn (1961) have presented the concept of symmetric dual programs, proving the point that the dual of the dual equals the primal. In 1968, Mond and Hanson extended symmetric duality to variational programs. Also many results have been extended by Hanson (1981), Mond and Smart (1988), Mond and Chandra (1988), Nahak and Nanda (1995) using invex functions, pseudo-invex functions, invexity and pseudo-invexity, as and when required. In this paper the authors apply the pseudo-invexity condition to symmetric dual variational problems studied by Smart and Mond (1990); the authors have presented some special cases of these problems under some reasonable assumptions.
scientific article; zbMATH DE number 1423585
scientific article