A class of nonconvex functions and pre-variational inequalities. (English) Zbl 0779.90067

Summary: A class of nonconvex functions is introduced, called semi-preinvex function, which includes the classes of preinvex functions and arc- connected convex functions. The Fritz-John conditions of the mathematical programming problem are derived for these kinds of functions. The pre- variational inequality is given as a necessary condition and also a sufficient condition for a mathematical programming for invex functions. The Type I function related to unconstrained problems is given as an equivalent form of the pre-variational inequality. Existence theorems for the solution of the pre-variational inequality are also proved.


90C26 Nonconvex programming, global optimization
26B25 Convexity of real functions of several variables, generalizations
49J40 Variational inequalities
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