Necessary Optimality Condition for Nonlinear Interval Vector Programming Problem Under B-Arcwise Connected Functions

2019 ◽  
pp. 649-659
Author(s):  
Mohan Bir Subba ◽  
Vinay Singh
Keyword(s):  
Programming Problem ◽  
Optimality Condition ◽  
Necessary Optimality Condition ◽  
Interval Vector ◽  
Arcwise Connected Functions ◽  
Arcwise Connected

scholarly journals A note on the paper "Optimality conditions for nonsmooth interval-valued and multiobjective semi-infinite programming"

2020 ◽  
Author(s):  
Nazih Abderrazzak Gadhi ◽  
Aissam Ichatouhane
Keyword(s):  
Optimality Conditions ◽  
Programming Problem ◽  
Optimality Condition ◽  
Short Proof ◽  
Necessary Optimality Condition ◽  
Main Result Theorem ◽  
Correct Formulation ◽  
Result Theorem ◽  
Infinite Programming ◽  
Interval Valued

A nonsmooth semi-infinite interval-valued vector programming problem is solved in the paper by Jennane et all. (RAIRO-Oper. Res. doi: 10.1051/ro/2020066, 2020). The necessary optimality condition obtained by the authors, as well as its proof, is false. Some counterexamples are given to refute some results on which the main result (Theorem 4.5) is based. For the convinience of the reader, we correct the faulty in those results, propose a correct formulation of Theorem 4.5 and give also a short proof.

scholarly journals A note on arewise connected sets and functions

1985 ◽  
Vol 31 (3) ◽  
pp. 369-375 ◽  
Author(s):  
Shri Ram Yadav ◽  
R.N. Mukherjee
Keyword(s):  
Mathematical Programming ◽  
Programming Problem ◽  
Mathematical Programming Problem ◽  
Basic Properties ◽  
New Class ◽  
Connected Sets ◽  
Arcwise Connected Functions ◽  
Arcwise Connected ◽  
Class Of Functions

We introduce a new class of generalized arcwise connected functions and discuss their basic properties. Our generalization is illustrated by an example and an application is given for a mathematical programming problem involving this new class of functions.

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

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.

scholarly journals Necessary optimality condition for trilevel optimization problem

2020 ◽  
Vol 16 (1) ◽  
pp. 55-70
Author(s):  
Gaoxi Li ◽  
◽  
Zhongping Wan ◽  
Jia-wei Chen ◽  
Xiaoke Zhao ◽  
...  
Keyword(s):  
Optimality Condition ◽  
Optimization Problem ◽  
Necessary Optimality Condition

Noether’s theorem for fractional variational problems of variable order

Open Physics ◽  
2013 ◽  
Vol 11 (6) ◽  
Author(s):  
Tatiana Odzijewicz ◽  
Agnieszka Malinowska ◽  
Delfim Torres
Keyword(s):  
Optimality Condition ◽  
Variational Problems ◽  
Time Variable ◽  
Variable Order ◽  
Necessary Optimality Condition ◽  
Noether’S Theorem ◽  
Noether's Theorem ◽  
Fractional Variational Problems ◽  
Derivatives Of

AbstractWe prove a necessary optimality condition of Euler-Lagrange type for fractional variational problems with derivatives of incommensurate variable order. This allows us to state a version of Noether’s theorem without transformation of the independent (time) variable. Considered derivatives of variable order are defined in the sense of Caputo.

scholarly journals A multiplier rule in set-valued optimisation

2003 ◽  
Vol 68 (1) ◽  
pp. 93-100 ◽  
Author(s):  
Akhtar A. Khan ◽  
Fabio Raciti
Keyword(s):  
Optimality Condition ◽  
Necessary Optimality Condition ◽  
Dini Derivative ◽  
Multiplier Rule

A multiplier rule is given as a necessary optimality condition for proper minimality in set-valued optimisation. We use derivatives in the sense of the lower Dini derivative for the objective set-valued map and the set-valued maps defining the constraints.

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