## Generalization of preinvex and B-vex functions.(English)Zbl 0802.49026

Summary: A class of functions called $$B$$-preinvex functions is introduced by relaxing the definitions of preinvex and $$B$$-vex functions. Examples are given to show that there exist functions which are $$B$$-preinvex but not preinvex or $$B$$-vex or quasipreinvex. Some of the properties of $$B$$-invex functions are obtained.

### MSC:

 49M37 Numerical methods based on nonlinear programming 49J52 Nonsmooth analysis 49K27 Optimality conditions for problems in abstract spaces

### Keywords:

$$B$$-preinvex functions; $$B$$-vex functions
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### References:

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