Topic
Invex function
About: Invex function is a research topic. Over the lifetime, 59 publications have been published within this topic receiving 2898 citations.
Papers published on a yearly basis
Papers
TL;DR: In this paper, it was shown that there are other wide classes of functions for which the pseudo-convexity of&(x) and quasiconvexeness off(x)-conditions are sufficient for optimality.
1,273 citations
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TL;DR: In this article, it was shown that invexity can be substituted for convexity in the saddle point problem and in the Slater constraint qualification for both constrained and unconstrained problems.
Abstract: Recently it was shown that many results in Mathematical Programming involving convex functions actually hold for a wider class of functions, called invex. Here a simple characterization of invexity is given for both constrained and unconstrained problems. The relationship between invexity and other generalizations of convexity is illustrated. Finally, it is shown that invexity can be substituted for convexity in the saddle point problem and in the Slater constraint qualification.
565 citations
TL;DR: In this article, a generalization of the mean value theorem is considered in the case of functions defined on an invex set with respect to η (which is not necessarily connected).
Abstract: In this paper, a generalization of the mean value theorem is considered in the case of functions defined on an invex set with respect to η (which is not necessarily connected).
173 citations
TL;DR: In this article, a generalization of the notion of p -invex sets with respect to η leads to a new class of functions, called (p, r )-pre-in-vex functions, and a family of real functions called, in general, (p, r ) − pre-invx functions with respect η (without differentiability) or ( p, r − v ) − v − invex (in the differentiable case) is introduced.
151 citations
1 Jan 1998
TL;DR: In this article, the main definitions of generalized convex and generalized invex vector functions are surveyed, and some other broad classes of generalized in-vex functions are introduced, both in the differentiable and nonsmooth case.
Abstract: After a survey of the main definitions of generalized convex and generalized invex vector functions, some other broad classes of generalized invex vector functions are introduced, both in the differentiable case and in the nonsmooth case. With reference to the said functions we extend some results of weak efficiency, efficiency and duality.
52 citations
Related Topics (5)
Performance Metrics
| Year | Papers |
|---|---|
| 2021 | 6 |
| 2020 | 1 |
| 2019 | 1 |
| 2018 | 1 |
| 2017 | 4 |
| 2016 | 4 |