In this paper, we investigate necessary and sufficient optimality conditions for mathematical programs with equilibrium constraints. For this goal, we introduce an appropriate type of MPEC regularity condition and a stationary concept given in terms of directional upper convexificators and directional upper semi-regular convexificators. The appearing functions are not necessarily smooth/locally Lipschitz/convex/continuous, and the continuity directions’ sets are not assumed to be compact or convex. Finally, notions of directional pseudoconvexity and directional quasiconvexity are used to establish sufficient optimality conditions for MPECs.
Keywords: Directional upper convexificators, directional upper semi-regular convexificators, regularity conditions, mathematical programs with equilibrium constraints, optimality conditions
@article{RO_2022__56_6_4303_0,
author = {Gadhi, Nazih Abderrazzak and Ohda, Mohamed},
title = {Optimality conditions for {MPECs} in terms of directional upper convexifactors},
journal = {RAIRO. Operations Research},
pages = {4303--4316},
year = {2022},
publisher = {EDP-Sciences},
volume = {56},
number = {6},
doi = {10.1051/ro/2022203},
mrnumber = {4523955},
zbl = {1536.90209},
language = {en},
url = {https://www.numdam.org/articles/10.1051/ro/2022203/}
}
TY - JOUR AU - Gadhi, Nazih Abderrazzak AU - Ohda, Mohamed TI - Optimality conditions for MPECs in terms of directional upper convexifactors JO - RAIRO. Operations Research PY - 2022 SP - 4303 EP - 4316 VL - 56 IS - 6 PB - EDP-Sciences UR - https://www.numdam.org/articles/10.1051/ro/2022203/ DO - 10.1051/ro/2022203 LA - en ID - RO_2022__56_6_4303_0 ER -
%0 Journal Article %A Gadhi, Nazih Abderrazzak %A Ohda, Mohamed %T Optimality conditions for MPECs in terms of directional upper convexifactors %J RAIRO. Operations Research %D 2022 %P 4303-4316 %V 56 %N 6 %I EDP-Sciences %U https://www.numdam.org/articles/10.1051/ro/2022203/ %R 10.1051/ro/2022203 %G en %F RO_2022__56_6_4303_0
Gadhi, Nazih Abderrazzak; Ohda, Mohamed. Optimality conditions for MPECs in terms of directional upper convexifactors. RAIRO. Operations Research, Tome 56 (2022) no. 6, pp. 4303-4316. doi: 10.1051/ro/2022203
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