On the Mangasarian–Fromovitz constraint qualification and Karush–Kuhn–Tucker conditions in nonsmooth semi-infinite multiobjective programming

We discuss constraint qualifications in Karush–Kuhn–Tucker multiplier rules in nonsmooth semi-infinite multiobjective programming. A version of the Manganarian–Fromovitz constraint qualification is proposed, in terms of the Michel–Penot directional derivative and the Studniarski derivative of order...

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Bibliographic Details
Published in:Optimization letters Vol. 14; no. 8; pp. 2055 - 2072
Main Authors: Khanh, Phan Quoc, Tung, Nguyen Minh
Format: Journal Article
Language:English
Published: Berlin/Heidelberg Springer Berlin Heidelberg 01.11.2020
Subjects:
Computational Intelligence
Mathematics
Mathematics and Statistics
Numerical and Computational Physics
Operations Research/Decision Theory
Optimization
Original Paper
Simulation
Optimality condition
Directional Hölder metric subregularity
Constraint qualification
Firm solution
Semi-infinite multiobjective programming
Proper solution
ISSN:1862-4472, 1862-4480
Online Access:Get full text
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Summary:We discuss constraint qualifications in Karush–Kuhn–Tucker multiplier rules in nonsmooth semi-infinite multiobjective programming. A version of the Manganarian–Fromovitz constraint qualification is proposed, in terms of the Michel–Penot directional derivative and the Studniarski derivative of order p which is just the order of the directional Hölder metric subregularity which is included also in this proposed qualification version. Using this qualification together with the Pshenichnyi–Levitin–Valadire property, we establish Karush–Kuhn–Tucker optimality conditions for Borwein-proper and firm solutions. We also compare in detail our qualification version with other usually-employed constraint qualifications. Applications to semi-infinite multiobjective fractional problems and minimax problems are provided.
ISSN:1862-4472
1862-4480
DOI:10.1007/s11590-019-01529-3