Open Access
Issue |
RAIRO-Oper. Res.
Volume 56, Number 6, November-December 2022
|
|
---|---|---|
Page(s) | 4303 - 4316 | |
DOI | https://doi.org/10.1051/ro/2022203 | |
Published online | 21 December 2022 |
- A.A. Ardali, N. Movahedian and S. Nobakhtian, Optimality conditions for nonsmooth mathematical programs with equilibrium constraints, using convexifactors. Optimization 65 (2016) 67–85. [Google Scholar]
- F.H. Clarke, Y.S. Ledyaev, R.J. Stren and P.R. Wolenski, Nonsmooth Analysis and Control Theory. New York, Springer-Verlag (1998). [Google Scholar]
- S. Dempe and M. Pilecka, Necessary optimality conditions for optimistic bilevel programming problems using set-valued programming. J. Glob. Optim. 61 (2015) 769–788. [CrossRef] [Google Scholar]
- V.F. Demyanov and V. Jeyakumar, Hunting for a Smaller Convex Subdifferential. J. Glob. Optim. 10 (1997) 305–326. [CrossRef] [Google Scholar]
- J. Dutta and S. Chandra, Convexifactors, generalized convexity, and optimality conditions. J. Optim. Theory Appl. 113 (2002) 41–64. [CrossRef] [MathSciNet] [Google Scholar]
- G.M. Ewing, Sufficient conditions for global minima of suitably convex functionals from variational and control theory. SIAM Rev. 19 (1977) 202–220. [Google Scholar]
- M.L. Flegel, Constraint Qualifications and Stationarity Concepts for Mathematical Programs with Equilibrium Constraints. Doctoral Dissertation, Universität Würzburg (2005). [Google Scholar]
- M.L. Flegel and C. Kanzow, A Fritz John approach to first-order optimality conditions for mathematical programs with equilibrium constraints. Optimization 52 (2003) 277–286. [CrossRef] [MathSciNet] [Google Scholar]
- M.L. Flegel and C. Kanzow, Abadie-Type constraint qualification for mathematical programs with equilibrium constraints. J. Optim. Theory Appl. 124 (2005) 595–614. [CrossRef] [MathSciNet] [Google Scholar]
- M.L. Flegel and C. Kanzow, On the guignard constraint qualification for mathematical programs with equilibrium constraints. Optimization 54 (2005) 517–534. [CrossRef] [MathSciNet] [Google Scholar]
- N.A. Gadhi, On variational inequalities using directional convexificators. Optimization 71 (2021) 2891–2905. [Google Scholar]
- N.A. Gadhi, A note on the paper “Necessary and sufficient optimality conditions using convexifactors for mathematical programs with equilibrium constraints”, RAIRO:RO 55 (2021) 3217–3223. [CrossRef] [EDP Sciences] [Google Scholar]
- N.A. Gadhi, Comments on “A note on the paper optimality conditions for optimistic bilevel programming problem using convexifactors”. J. Optim. Theory Appl. 189 (2021) 938–943. [CrossRef] [MathSciNet] [Google Scholar]
- N. Gadhi, F. Rahou, M. El idrissi and L. Lafhim, Optimality conditions of a set valued optimization problem with the help of directional convexificators. optimization 70 (2021) 575–590. [CrossRef] [MathSciNet] [Google Scholar]
- J.B. Hiriart-Urruty and C. Lemarechal, Fundamentals of Convex Analysis. Springer-Verlag, Berlin Heidelberg (2001). [CrossRef] [Google Scholar]
- V. Jeakumar and D.T. Luc, Nonsmooth Calculus, Minimality, and Monotonicity of Convexificators. J. Optim. Theory Appl. 101 (1999) 599–621. [CrossRef] [MathSciNet] [Google Scholar]
- A. Kabgani and M. Soleimani-damaneh, Characterization of (weakly/properly/robust) efficient solutions in nonsmooth semiinfinite multiobjective optimization using convexificators. Optimization 67 (2017) 217–235. [Google Scholar]
- A. Kabgani and M. Soleimani-damaneh, Constraint qualifications and optimality conditions in nonsmooth locally star-shaped optimization using convexificators. Pac. J. Optim. 15 (2019) 399–413. [MathSciNet] [Google Scholar]
- N. Kanzi and S. Nobakhtian, Optimality conditions for nonsmooth semi-infinite multiobjective programming. Optim. Lett. 8 (2014) 1517–1528. [CrossRef] [MathSciNet] [Google Scholar]
- B. Kohli, Necessary and sufficient optimality conditions using convexifactors for mathematical programs with equilibrium constraints. RAIRO:RO 53 (2019) 1617–1632. [CrossRef] [EDP Sciences] [Google Scholar]
- S. Kaur, Theoretical studies in mathematical programming. Ph.D. thesis, University of Delhi, (1983). [Google Scholar]
- X.F. Li and J.Z. Zhang, Necessary optimality conditions in terms of convexificators in Lipschitz optimization. J. Optim. Theory Appl. 131 (2006) 429–452. [CrossRef] [MathSciNet] [Google Scholar]
- J.E. Martnez-Legaz, Optimality conditions for pseudoconvex minimization over convex sets defined by tangentially convex constraints. Optim. Lett. 9 (2015) 1017–1023. [Google Scholar]
- B.S. Mordukhovich and Y. Shao, On nonconvex subdifferential calculus in Banach spaces. J. Convex Anal. 2 (1995) 211–227. [MathSciNet] [Google Scholar]
- J.-P. Penot and P. Michel, A generalized derivative for calm and stable functions. Differ. Integral Equ. 5 (1992) 433–454. [Google Scholar]
- R.T. Rockafellar, Convex Analysis. Princeton, New Jersey (1970). [Google Scholar]
- R.T. Rockafellar and R. Wets, Variational Analysis. Series: Grundlehren der mathematischen Wissenschaften (2009) 317. [Google Scholar]
- J.J. Ye, Necessary and sufficient optimality conditions for mathematical programs with equilibrium constraints. J. Math. Anal. Appl. 307 (2005) 350–369. [CrossRef] [MathSciNet] [Google Scholar]
Current usage metrics show cumulative count of Article Views (full-text article views including HTML views, PDF and ePub downloads, according to the available data) and Abstracts Views on Vision4Press platform.
Data correspond to usage on the plateform after 2015. The current usage metrics is available 48-96 hours after online publication and is updated daily on week days.
Initial download of the metrics may take a while.