A critical view on invexity

The aim of this note is to emphasize the fact that in many papers on invexity published in prestigious journals there are not clear definitions, trivial or not clear statements and wrong proofs. We also point out the unprofessional way of answering readers' questions by some authors. We think that this is caused mainly by the lack of criticism of the invexity communityComment: The paper was submitted to JOTA in December 2007 and practically accepted by the AE handling it in March 2008. Being a critical paper, the EiC asked the authors of the criticised articles to say their opinion. With the change of the EiC's, apparently the paper was not transmitted to the new Ei

New classes of higher order variational-like inequalities

In this paper, we prove that the optimality conditions of the higher order convex functions are characterized by a class of variational inequalities, which is called the higher order variational inequality. Auxiliary principle technique is used to suggest an implicit method for solving higher order variational inequalities. Convergence analysis of the proposed method is investigated using the pseudo-monotonicity of the operator. Some special cases also discussed. Results obtained in this paper can be viewed as refinement and improvement of previously known results

NEW ASPECTS OF STRONGLY Log-PREINVEX FUNCTIONS

In this paper, we consider some new classes of log-preinvex functions. Several properties of the log-preinvex functions are studied. We also discuss their relations with convex functions. Several interesting results characterizing the log-convex functions are obtained. Optimality conditions of differentiable strongly $\log$-preinvex are characterized by a class of variational-like inequalities.  Results obtained in this paper can be viewed as significant improvement of previously known results