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γ-preinvexity andγ-invexity in mathematical programming

Authors
Journal
Computers & Mathematics with Applications
0898-1221
Publisher
Elsevier
Publication Date
Volume
50
Identifiers
DOI: 10.1016/j.camwa.2005.01.024
Keywords
  • γ-Preinvex Function
  • γ-Invex Function
  • Optimality Conditions
  • Wolfe Duality
  • Alternative Approach
Disciplines
  • Computer Science
  • Mathematics

Abstract

Abstract In the paper, we introduce and characterize a new class of nonconvex functions in mathematical programming, named γ-preinvex functions, which are called γ-invex functions in the case of differentiability. The class of γ-reinvex functions is wider than that of preinvex functions and thus, in the case of differentiability, than the class of invex functions. Some optimality results are obtained under γ-preinvexity assumption for a constrained optimization problem with not necessarily differentiable functions. Further, a number of sufficiency conditions and Wolfe duality theorems are established under γ-invexity assumption. An alternative approach with a modified γ-invexity notion to optimality conditions and duality results is also considered.

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