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# Generalized (ρ,θ)-η-invexity and generalized (ρ,θ)-η-invariant-monotonicity

Department of Mathematics, Indian Institute of Technology, Kharagpur 721302, India

Nonlinear Analysis: Theory, Methods & Applications 01/2008; DOI: 10.1016/j.na.2007.02.004 - Citations (10)
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**ABSTRACT:**A class of functions, called pre-invex, is defined. These functions are more general than convex functions and when differentiable are invex. Optimality conditions and duality theorems are given for both scalar-valued and vector-valued programs involving pre-invex functions.Bulletin of the Australian Mathematical Society 09/1988; 38(02):177 - 189. · 0.48 Impact Factor -
##### Article: Seven kinds of monotone maps

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**ABSTRACT:**Known as well as new types of monotone and generalized monotone maps are considered. For gradient maps, these generalized monotonicity properties can be related to generalized convexity properties of the underlying function. In this way, pure first-order characterizations of various types of generalized convex functions are obtained.Journal of Optimization Theory and Applications 06/1990; 66(1):37-46. · 1.42 Impact Factor - [Show abstract] [Hide abstract]

**ABSTRACT:**Generalized monotonocity of bifunctions or multifunctions is a rather new concept in optimization and nonsmooth analysis. It is shown in the present paper how quasiconvexity, pseudoconvexity, and strict pseudoconvexity of lower semicontinuous functions can be characterized via the quasimonotonicity, pseudomonotonicity, and strict pseudomonotonicity of different types of generalized derivatives, including the Dini, Dini-Hadamard, Clarke, and Rockafellar derivatives as well.Journal of Optimization Theory and Applications 01/1995; 84(2):361-376. · 1.42 Impact Factor

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