## $$(p,r)$$-invex sets and functions.(English)Zbl 1051.90018

Summary: Notions of invexity of a function and of a set are generalized. The notion of an invex function with respect to $$\eta$$ can be further extended with the aid of $$p$$-invex sets. Slight generalization of the notion of $$p$$-invex sets with respect to $$\eta$$ leads to a new class of functions. A family of real functions called, in general, $$(p, r)$$-pre-invex functions with respect to $$\eta$$ (without differentiability) or $$(p,r)$$-invex functions with respect to $$\eta$$ (in the differentiable case) is introduced. Some (geometric) properties of these classes of functions are derived. Sufficient optimality conditions are obtained for a nonlinear programming problem involving $$(p, r)$$-invex functions with respect to $$\eta$$ .

### MSC:

 90C26 Nonconvex programming, global optimization 26B25 Convexity of real functions of several variables, generalizations 90C29 Multi-objective and goal programming
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### References:

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