Monotonicity in the Framework of Generalized Convexity

Semi-infinite minimax fractional programming problems with both inequality and equality constraints are considered. The sets of parametric saddle point conditions are established for a new class of nonconvex differentiable semi-infinite minimax fractional programming problems under(?,?)-invexity assumptions. With the reference to the said concept of generalized convexity, we extend some results of saddle point criteria for a larger class of nonconvex semi-infinite minimax fractional programming problems in comparison to those ones previously established in the literature.

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Second order duality for variational problems involving generalized convexity

OPSEARCH ◽

10.1007/s12597-014-0195-0 ◽

2014 ◽

Vol 52 (3) ◽

pp. 582-596 ◽

Cited By ~ 3

Author(s):

Anurag Jayswal ◽

I. M. Stancu-Minasian ◽

Sarita Choudhury

Keyword(s):

Generalized Convexity ◽

Variational Problems ◽

Second Order ◽

Second Order Duality

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A Generalized Convexity and Variational Inequality for Quasi-Convex Minimization

SIAM Journal on Optimization ◽

10.1137/0806012 ◽

1996 ◽

Vol 6 (1) ◽

pp. 212-226 ◽

Cited By ~ 4

Author(s):

Phan Thien Thach ◽

Masakazu Kojima

Keyword(s):

Variational Inequality ◽

Generalized Convexity ◽

Convex Minimization

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Convexifactors, generalized convexity and vector optimization

Optimization ◽

10.1080/02331930410001661505 ◽

2004 ◽

Vol 53 (1) ◽

pp. 77-94 ◽

Cited By ~ 27

Author(s):

J. Dutta ◽

S. Chandra

Keyword(s):

Vector Optimization ◽

Generalized Convexity

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Optimality of Approximate Quasi-Weakly Efficient Solutions for Vector Equilibrium Problems via Convexificators

Asia Pacific Journal of Operational Research ◽

10.1142/s0217595921500470 ◽

2021 ◽

Author(s):

Guolin Yu ◽

Siqi Li ◽

Xiao Pan ◽

Wenyan Han

Keyword(s):

Optimality Condition ◽

Generalized Convexity ◽

Equilibrium Problems ◽

Efficient Solutions ◽

Sufficient Optimality Condition ◽

Necessary Optimality Condition ◽

Weakly Efficient Solutions ◽

Convexity Assumption ◽

Pseudoconvex Function ◽

Vector Equilibrium

This paper is devoted to the investigation of optimality conditions for approximate quasi-weakly efficient solutions to a class of nonsmooth Vector Equilibrium Problem (VEP) via convexificators. First, a necessary optimality condition for approximate quasi-weakly efficient solutions to problem (VEP) is presented by making use of the properties of convexificators. Second, the notion of approximate pseudoconvex function in the form of convexificators is introduced, and its existence is verified by a concrete example. Under the introduced generalized convexity assumption, a sufficient optimality condition for approximate quasi-weakly efficient solutions to problem (VEP) is also established. Finally, a scalar characterization for approximate quasi-weakly efficient solutions to problem (VEP) is obtained by taking advantage of Tammer’s function.

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