TY - JOUR
ID - 6803
TI - Unified duality for mathematical programming problems with vanishing constraints
JO - International Journal of Nonlinear Analysis and Applications
JA - IJNAA
LA - en
SN - 2008-6822
AU - Ahmad, Izhar
AU - Kummari, Krishna
AU - Al-Homidan, S
AD - Department of Mathematics, King Fahd University of Petroleum and Minerals, Dhahran 31261, Saudi Arabia
AD - Department of Mathematics, School of Science, GITAM-Hyderabad Campus Hyderabad-502329, India
Y1 - 2022
PY - 2022
VL - 13
IS - 2
SP - 3191
EP - 3201
KW - Mathematical programming problem
KW - vanishing constraints
KW - Constraint Qualifications
KW - duality
DO - 10.22075/ijnaa.2022.25816.3134
N2 - In this article, we formulate a new mixed-type dual problem for a mathematical program with vanishing constraints. The presented dual problem does not involve the index set, however, the dual models contain the calculations of index sets, which makes it difficult to solve these models from an algorithm point of view. The weak, strong and strict converse duality theorems are discussed in order to establish the relationships between the mathematical program with vanishing constraints and its mixed type dual under generalized convexity. To validate the results, a non-trivial example is discussed. Our dual model unifies the dual models discussed in [Q. Hu, J. Wang, Y. Chen, New dualities for mathematical programs with vanishing constraints, Annals of Operations Research, 287 (2020) 233-255].
UR - https://ijnaa.semnan.ac.ir/article_6803.html
L1 - https://ijnaa.semnan.ac.ir/article_6803_c9f5f83149a7991849846a81a29a0ce7.pdf
ER -