In the paper we generalize sufficient and necessary optimality conditions obtained by Ginchev, Guerraggio, Rocca, and by authors with the help of the notion of
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@article{RO_2009__43_4_359_0, author = {Bedna\v{r}{\'\i}k, Du\v{s}an and Pastor, Karel}, title = {Decrease of $C^{1,1}$ property in vector optimization}, journal = {RAIRO - Operations Research - Recherche Op\'erationnelle}, pages = {359--372}, publisher = {EDP-Sciences}, volume = {43}, number = {4}, year = {2009}, doi = {10.1051/ro/2009023}, mrnumber = {2573992}, language = {en}, url = {https://www.numdam.org/articles/10.1051/ro/2009023/} }
TY - JOUR AU - Bednařík, Dušan AU - Pastor, Karel TI - Decrease of $C^{1,1}$ property in vector optimization JO - RAIRO - Operations Research - Recherche Opérationnelle PY - 2009 SP - 359 EP - 372 VL - 43 IS - 4 PB - EDP-Sciences UR - https://www.numdam.org/articles/10.1051/ro/2009023/ DO - 10.1051/ro/2009023 LA - en ID - RO_2009__43_4_359_0 ER -
%0 Journal Article %A Bednařík, Dušan %A Pastor, Karel %T Decrease of $C^{1,1}$ property in vector optimization %J RAIRO - Operations Research - Recherche Opérationnelle %D 2009 %P 359-372 %V 43 %N 4 %I EDP-Sciences %U https://www.numdam.org/articles/10.1051/ro/2009023/ %R 10.1051/ro/2009023 %G en %F RO_2009__43_4_359_0
Bednařík, Dušan; Pastor, Karel. Decrease of $C^{1,1}$ property in vector optimization. RAIRO - Operations Research - Recherche Opérationnelle, Tome 43 (2009) no. 4, pp. 359-372. doi : 10.1051/ro/2009023. https://www.numdam.org/articles/10.1051/ro/2009023/
[1] Differential inclusions, Springer Verlag, Berlin (1984). | MR | Zbl
and ,[2] On characterization of convexity for regularly locally Lipschitz functions. Nonlinear Anal. 57 (2004) 85-97. | MR | Zbl
and ,[3] Elimination of strict convergence in optimization. SIAM J. Control Optim. 43 (2004) 1063-1077. | MR | Zbl
and ,[4] Using the Peano derivative in unconstrained optimization. Math. Program. 113 (2008) 283-298. | Zbl
and ,
[5] Differentiability properties of functions that are
[6]
[7] Directional derivatives in nonsmooth optimization. J. Optim. Theory Appl. 47 (1985) 483-490. | MR | Zbl
and ,[8] On generalized second-order derivatives and Taylor expansions in nonsmooth optimization. SIAM J. Control Optim. 32 (1994) 591-611. | MR | Zbl
, and ,[9] A generalized second-order derivative in nonsmooth optimization. SIAM J. Control Optim. 28 (1990) 789-809. | MR | Zbl
and ,
[10] Second-order Subdifferentials of
[11] Higher order optimality conditions in nonsmooth optimization. Optimization 51 (2002) 47-72. | MR | Zbl
,
[12] Second order conditions for
[13] From scalar to vector optimization. Applications of Mathematics 51 (2006) 5-36. | MR | Zbl
, and ,
[14] Optimality conditions for
[15] Generalized Hessian matrix and second order optimality conditions for problems with
[16] On lower bounds of the second-order directional derivatives of Ben-Tal-Zowe and Chaney. Math. Oper. Res. 22 (1997) 747-753. | MR | Zbl
and ,[17] Vector optimization, Springer Verlag, New York (2004). | MR | Zbl
,[18] First and second order sufficient conditions for strict minimality in nonsmooth vector optimization. J. Math. Anal. Appl. 284 (2003) 496-510. | MR | Zbl
and ,[19] First order optimality conditions in vector optimization involving stable functions. Optimization 57 (2008) 449-471. | MR
and ,[20] Optimality conditions for nonsmooth multiobjective optimization using Hadamard directional derivatives. J. Optim. Theory Appl. 133 (2007) 341-357. | MR | Zbl
and ,
[21] Upper Lipschitz behavior of solutions to perturbed
[22] The second-order conditions of nondominated solutions for
[23] The second-order optimality conditions for nonlinear mathematical programming with
[24] Second-order optimality conditions for nondominated solutions of multiobjective programming with
[25] Second-order necessary conditions for nonlinear optimization problems in Banach spaces and their application to an optimal control problem. Math. Oper. Res. 15 (1990) 467-482. | MR | Zbl
,[26] Convexity and generalized second-order derivatives for locally Lipschitz functions. Nonlinear Anal. 60 (2005) 547-555. | MR | Zbl
,[27] Fréchet approach to generalized second-order differentiability. to appear in Studia Scientiarum Mathematicarum Hungarica 45 (2008) 333-352.
,[28] Convex analysis, Princeton University Press, Princeton (1970). | MR | Zbl
,[29] Variational Analysis, Springer Verlag, New York (1998). | MR | Zbl
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