Necessary and Sufficient Optimality Conditions for Semi-infinite Programming with Multiple Fuzzy-valued Objective Functions
Abstract
This paper deals with semi-infifinite programming with multiple fuzzy-valued objective functions. Firstly, some types of effificient solutions are proposed and illustrated in some examples. Then, necessary and suffificient Karush-Kuhn-Tucker optimality conditions for semi-infifinite programming with multiple fuzzy-valued objective functions are established.References
J.P. Aubin, and H. Frankowska, Set-Valued Analysis, Birkh¨auser, Boston, 1990.
Y. Chalco-Cano, W.A. Lodwick, R. Osuna-G´omez, and A. Rufi´an-Lizana, The Karush-Kuhn-Tucker optimality conditions for fuzzy optimization problems, Fuzzy Optimization and Decision Making, vol. 15, pp. 57–73, 2016.
S. Chen, The KKT optimality conditions for optimization problem with interval-valued objective function on Hadamard manifolds, Optimization, doi: 10.1080/02331934.2020.1810248
T.D. Chuong, and D.S. Kim, Nonsmooth semi-infinite multiobjective optimization problems, Journal of Optimization Theory and Applications, vol. 160, pp. 748–762, 2014.
T.D. Chuong, and J.C. Yao, Isolated and proper efficiencies in semi-infinite vector optimization problems, Journal of Optimization Theory and Applications, vol. 162, pp. 447–462, 2014.
M.A. Goberna, and M.A. L´opez, Linear Semi-Infinite Optimization, Wiley, Chichester, 1998.
M.A. Goberna, and N. Kanzi, Optimality conditions in convex multiobjective SIP, Mathematical Programming, vol. 164, pp. 67–191, 2017.
J.B. Hiriart-Urruty, and C. Lemar´echal, Convex Analysis and Minimization Algorithms I, Springer, Berlin, 1993.
B. Jim´enez, Strict efficiency in vector optimization, Journal of Mathematical Analysis and Applications, vol. 265, no. 2, pp. 264–284, 2002.
N. Kanzi, Lagrange multiplier rules for non-differentiable DC generalized semi-infinite programming problems, Journal of Global Optimization, vol. 56, pp. 417–430, 2013.
N. Kanzi, and S. Nobakhtian, Optimality conditions for nonsmooth semi-infinite multiobjective programming, Optimization Letters, vol. 8, pp. 1517–1528, 2014.
O. Kostyukova, T. Tchemisova, and M. Kurdina, Existence theorem and optimality conditions for a class of convex semi-infinite problems with noncompact index sets, Statistics, Optimization & Information Computing, vol. 5, no. 4, pp. 278–294, 2017.
O. Kostyukova, and T. Tchemisova, Algorithmic determination of immobile indices in convex SIP problems with polyhedral index sets, INFOR: Information Systems and Operational Research, vol. 58, no. 2, pp. 182–201, 2020.
D.T. Luc, Theory of Vector Optimization, Springer, Berlin, 1989.
S. Mehrotra, and D. Papp, A cutting surface algorithm for semi-infinite convex programming with an application to moment robust optimization, SIAM Journal on Optimization, vol. 24, no. 4, pp. 1670–1697, 2014.
B.S. Mordukhovich, and T.T.A. Nghia, Constraint qualifications and optimality conditions in semi-infinite and infinite programming, Mathematical Programming, vol. 139, pp. 271–300, 2013.
B.S. Mordukhovich, Variational Analysis and Applications Springer, New York, 2018.
R. Osuna-G´omez, Y. Chalco-Cano, A. Rufi´an-Lizana, and B. Hern´adez-Jim´enez, Necessary and suffcient conditions for fuzzy optimality problems, Fuzzy Sets and Systems, vol. 296, pp. 112–123, 2016.
R. Osuna-G´omez, B. Hern´adez-Jim´enez, Y. Chalco-Cano, and G. Ruiz-Garz´on, New optimality conditions for multiobjective fuzzy programming problems, Iranian Journal of Fuzzy Systems, vol. 17, no. 3, pp. 19–31, 2020.
A.W. Potchinkov, and R.M. Reemtsen, The simultaneous approximation of magnitude and phase by FIR digital filters. I: A new approach, International Journal of Circuit Theory and Applications, vol. 25, no. 3, pp. 167–177, 1997.
M. Rahimi, and M. Soleimani-damaneh, Isolated efficiency in nonsmooth semi-infinite multi-objective programming, Optimization, vol. 67, no. 11, pp. 1923–1947, 2018.
R.T. Rockafellar, Convex Analysis, Princeton Mathematical Series, vol. 28, Princeton University Press, Princeton, New Jersey, 1970.
L. Stefanini, and M. Arana-Jim´enez, Karush-Kuhn-Tucker conditions for interval and fuzzy optimization in several variables under total and directional generalized differentiability, Fuzzy Sets and Systems, vol. 362, pp. 1–34, 2019.
L.T. Tung, Strong Karush-Kuhn-Tucker optimality conditions for multiobjective semi-infinite programming via tangential
subdifferential, RAIRO-Operations Research, vol. 52, no. 4–5, pp. 1019–1041, 2018.
L.T. Tung, Karush-Kuhn-Tucker optimality conditions and duality for semi-infinite programming with multiple interval-valued objective functions, Journal of Nonlinear Functional Analysis, vol. 2019, pp. 1–21, 2019.
L.T. Tung, Karush-Kuhn-Tucker optimality conditions and duality for convex semi-infinite programming with multiple intervalvalued objective functions, Journal of Applied Mathematics and Computing, vol. 62, pp. 67–91, 2020.
L.T. Tung, Karush-Kuhn-Tucker optimality conditions and duality for semi-infinite programming problems with vanishing
constraints, Journal of Nonlinear and Variational Analysis, vol. 4, no. 3, pp. 319–336, 2020.
L.T. Tung, Karush-Kuhn-Tucker optimality conditions and duality for multiobjective semi-infinite programming with vanishing constraints, Annals of Operations Research, doi: 10.1007/s10479-020-03742-1
A.I.F. Vaz, E.M. Fernandes, and M.P.S. Gomes, Robot trajectory planning with semi-infinite programming, European Journal of Operational Research, vol. 153, no. 3, pp. 607–617, 2004.
A.I.F. Vaz, and E.C. Ferreira, Air pollution control with semi-infinite programming, Applied Mathematical Modelling, vol. 33, no. 4, pp. 1957–1969, 2009.
H.C. Wu, The Karush-Kuhn-Tucker optimality conditions for the optimization problem with fuzzy-valued objective function, Mathematical Methods of Operations Research, vol. 66, pp. 203–224, 2007.
H.C. Wu, The Karush-Kuhn-Tucker optimality conditions for multi-objective programming problems with fuzzy-valued objective functions, Fuzzy Optimization and Decision Making, vol. 8, pp. 1–28, 2009.
L.A. Zadeh, Fuzzy sets, Information and Control, vol. 8, pp. 338–353, 1965.
- Authors retain copyright and grant the journal right of first publication with the work simultaneously licensed under a Creative Commons Attribution License that allows others to share the work with an acknowledgement of the work's authorship and initial publication in this journal.
- Authors are able to enter into separate, additional contractual arrangements for the non-exclusive distribution of the journal's published version of the work (e.g., post it to an institutional repository or publish it in a book), with an acknowledgement of its initial publication in this journal.
- Authors are permitted and encouraged to post their work online (e.g., in institutional repositories or on their website) prior to and during the submission process, as it can lead to productive exchanges, as well as earlier and greater citation of published work (See The Effect of Open Access).