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$(p,r)$-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:
90C26Nonconvex programming, global optimization
26B25Convexity and generalizations (several real variables)
90C29Multi-objective programming; goal programming
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References:
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