Higher Order Convexity and Duality in Multiobjective Programming Problems

1999 ◽  
pp. 101-117 ◽  
Author(s):  
J. Zhang
Keyword(s):  
Multiobjective Programming ◽  
Higher Order ◽  
Multiobjective Programming Problems ◽  
Higher Order Convexity

scholarly journals Higher-order duality results for a new class of nonconvex nonsmooth multiobjective programming problems

Filomat ◽  
2019 ◽  
Vol 33 (6) ◽  
pp. 1619-1639
Author(s):  
Tadeusz Antczak ◽  
Hachem Slimani
Keyword(s):  
Multiobjective Programming ◽  
Vector Optimization Problem ◽  
Order Type ◽  
Higher Order ◽  
Type I ◽  
New Class ◽  
Duality Results ◽  
Nonsmooth Multiobjective Programming ◽  
Multiobjective Programming Problem ◽  
Multiobjective Programming Problems

In this paper, a nonconvex nonsmooth multiobjective programming problem is considered and two its higher-order duals are defined. Further, several duality results are established between the considered nonsmooth vector optimization problem and its dual models under assumptions that the involved functions are higher-order (??)-type I functions.

scholarly journals Pointwise estimates for higher order convexity preserving polynomial approximation

1994 ◽  
Vol 36 (2) ◽  
pp. 213-233 ◽  
Author(s):  
Jia-Ding Cao ◽  
Heinz H. Gonska
Keyword(s):  
Polynomial Approximation ◽  
Convex Functions ◽  
Higher Order ◽  
Second Order ◽  
Convolution Type ◽  
Shape Preservation ◽  
Moduli Of Continuity ◽  
Pointwise Estimates ◽  
Higher Order Convexity ◽  
Boolean Sum

AbstractDeVore-Gopengauz-type operators have attracted some interest over the recent years. Here we investigate their relationship to shape preservation. We construct certain positive convolution-type operators Hn, s, j which leave the cones of j-convex functions invariant and give Timan-type inequalities for these. We also consider Boolean sum modifications of the operators Hn, s, j show that they basically have the same shape preservation behavior while interpolating at the endpoints of [−1, 1], and also satisfy Telyakovskiῐ- and DeVore-Gopengauz-type inequalities involving the first and second order moduli of continuity, respectively. Our results thus generalize related results by Lorentz and Zeller, Shvedov, Beatson, DeVore, Yu and Leviatan.

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