Relationships between pre-invex concepts. (English) Zbl 1103.90398

Summary: It is well known that some properties of convex optimization problems, especially sufficient conditions for optimality, and duality conditions, are preserved when convexity is weakened to pre-invexity. However, there are several distinct pre-invex concepts-\(B\)-vex, \(B\)-pre-invex, pre-univex, \((p,r)\)-pre-invex-and these are not equivalent. The pre-invexity concepts mentioned above have also some properties which are characteristic and invariant for functions belonging to these classes of functions.


90C30 Nonlinear programming
90C25 Convex programming
90C26 Nonconvex programming, global optimization
52A01 Axiomatic and generalized convexity
52A40 Inequalities and extremum problems involving convexity in convex geometry
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