Acknowledgement
The authors are grateful to anonymous referees for their helpful suggestions and comments, which helped in the enhancement of this paper.
References
- I.Ahmad, A.Jayswal and J.Banerjee, On interval-valued optimization problems with generalized invex functions, J. Inequal. Appl. 2013 (1) (2013), 1-14. https://doi.org/10.1186/1029-242X-2013-1
- I.Ahmad, K.Kummari and S.Al-Homidan, Sufficiency and duality for interval-valued optimization problems with vanishing constraints using weak constraint qualifications, Internat. J. Anal. Appl. 18 (5) (2020), 784-798.
- H.Azimian, R.V.Patel, M.D.Naish and B.Kiaii, A semi-infinite programming approach to preoperative planning of robotic cardiac surgery under geometric uncertainty, IEEE J. Biomed. Health Inform. 17 (1) (2012), 172-182. https://doi.org/10.1109/TITB.2012.2220557
- C.Bandi and D.Bertsimas, Tractable stochastic analysis in high dimensions via robust optimization, Math. Program. 134 (1) (2012), 23-70. https://doi.org/10.1007/s10107-012-0567-2
- A.Ben-Tal, L.El.Ghaoui and A.Nemirovski, Robust Optimization, Princeton Series in Applied Mathematics. Princeton University Press, Princeton, NJ, USA, (2009).
- A.Ben-Tal and A.Nemirovski, Selected topics in robust convex optimization, Math. Program. 112 (1) (2008), 125-158. https://doi.org/10.1007/s10107-006-0092-2
- D.Bertsimas, D.B.Brown and C.Caramanis, Theory and applications of robust optimization, SIAM Rev. 53 (3) (2011), 464-501. https://doi.org/10.1137/080734510
- S.I.Birbil, J.B.G.Frenk, J.A.Gromicho and S.Zhang, The role of robust optimization in single-leg airline revenue management, Management Sci. 55 (1) (2009), 148-163. https://doi.org/10.1287/mnsc.1070.0843
- A.K.Bhurjee and G.Panda, Efficient solution of interval optimization problem, Math. Methods Oper. Res. 76 (3) (2012), 273-288. https://doi.org/10.1007/s00186-012-0399-0
- J.F.Bonnans and A.Shapiro, Perturbation Analysis of Optimization Problems, New York and Springer, (2013).
- C.Caramanis, S.Mannor and H.Xu, 14 Robust optimization in machine learning, In: S.Sra, S.Nowozin and S.J.Wright (editors). Optimization for Machine Learning, MIT Press, (2012), 369-402.
- A.Charnes, W.W.Cooper and K.Kortanek, A duality theory for convex programs with convex constraints, Bull. Amer. Math. Soc. 68 (6) (1962), 605-608. https://doi.org/10.1090/S0002-9904-1962-10870-2
- S.L.Chen, The KKT optimality conditions for optimization problem with interval-valued objective function on Hadamard manifolds, Optimization. 71 (3) (2022), 613-632. https://doi.org/10.1080/02331934.2020.1810248
- B.A.Dar, A.Jayswal and D.Singh, Optimality, duality and saddle point analysis for intervalvalued non-differentiable multi-objective fractional programming problems, Optimization. 70 (5-6) (2021), 1275-1305. https://doi.org/10.1080/02331934.2020.1819276
- V.Gabrel, C.Murat and A.Thiele, Recent advances in robust optimization: An overview, European J. Oper. Res. 235 (3) (2014), 471-483. https://doi.org/10.1016/j.ejor.2013.09.036
- M.Goerigk and A.Schobel, Algorithm engineering in robust optimization, In: L.Kliemann and P.Sanders (editors). Algorithm Engineering, Lect. Notes Comput. Sci. Springer, Cham, (2016), 245-279.
- R.Hettich and K.O.Kortanek, Semi-infinite programming: theory, methods and applications, SIAM Rev. 35 (3) (1993), 380-429. https://doi.org/10.1137/1035089
- A.Hussain, V.H.Bui and H.M.Kim, Robust optimization-based scheduling of multi-microgrids considering uncertainties, Energies 9 (4) (2016), 278. https://doi.org/10.3390/en9040278
- A.Jayswal, J.Banerjee and R.Verma, Some relations between interval-valued optimization and variational-like inequality problems, Comm. Appl. Nonlinear Anal. 20 (4) (2013), 47-56.
- V.Jeyakumar, G.M.Lee and G.Li, Characterizing robust solution sets of convex programs under data uncertainty, J. Optim. Theory Appl. 164 (2) (2015), 407-435. https://doi.org/10.1007/s10957-014-0564-0
- K.O.Kortanek and V.G.Medvedev, Semi-infinite programming and applications in finance, In: C.A.Floudas, P.M. Pardalos(editors). Encyclopaedia of Optimization, Boston and Springer, MA, (2008).
- P.Kumar and J.Dagar, Optimality and duality for multi-objective semi-infinite variational problem using higher-order B-type I functions, J. Oper. Res. Soc. China 9 (2) (2021), 375-393. https://doi.org/10.1007/s40305-019-00269-6
- P.Kumar, B.Sharma and J.Dagar, Multiobjective semi-infinite variational problem and generalized invexity, Opsearch 54 (3) (2017), 580-597. https://doi.org/10.1007/s12597-016-0293-2
- K.Kummari and I.Ahmad, Sufficient optimality conditions and duality for non-smooth intervalvalued optimization problems via L-invex-infine functions, Politehn. Univ. Bucharest Sci. Bull. Ser. A Appl. Math. Phys. 82 (1) (2020), 45-54.
- K.K.Lai, S.Y.Wang, J.P.Xu, S.S.Zhu and Y.Fang, A class of linear interval programming problems and its application to portfolio selection, IEEE Trans. Fuzzy Syst. 10 (6) (2002), 698-704. https://doi.org/10.1109/TFUZZ.2002.805902
- J.H.Lee and G.M.Lee, On optimality conditions and duality theorems for robust semi-infinite multi-objective optimization problems, Ann. Oper. Res. 269 (1) (2018), 419-438. https://doi.org/10.1007/s10479-016-2363-5
- J.Lin, M.Liu, J.Hao and S.Jiang, A multi-objective optimization approach for integrated production planning under interval uncertainties in the steel industry, Comput. Oper. Res. 72 (2016), 189-203. https://doi.org/10.1016/j.cor.2016.03.002
- M.S.Pishvaee, M.Rabbani and S.A.Torabi, A robust optimization approach to closed-loop supply chain network design under uncertainty, Appl. Math. Model. 35 (2) (2011), 637-649. https://doi.org/10.1016/j.apm.2010.07.013
- E.Polak, Semi-infinite optimization in engineering design, In: A.V.Fiacco and K.O.Kortanek (editors). Semi-Infinite Programming and Applications, Lect. Notes Econ. Math. Syst. Berlin and Springer, 215 (1983).
- E.W.Sachs, Semi-infinite programming in control, In: R.Reemtsen, J.J.Ruckmann (editors). Semi-Infinite Programming (Nonconvex Optimization and its Applications). Boston and Springer, MA, 25 (1998), 389-411.
- A.A.Shaikh, L.E.Cardenas-Barron and S.Tiwari, A two-warehouse inventory model for noninstantaneous deteriorating items with interval-valued inventory costs and stock-dependent demand under inflationary conditions, Neural. Comput. Appl. 31 (6) (2019), 1931-1948. https://doi.org/10.1007/s00521-017-3168-4
- Y.Shi, T.Boudouh and O.Grunder, A robust optimization for a home health care routing and scheduling problem with consideration of uncertain travel and service times, Transp. Res. E Logist. Transp. Rev. 128 (2019), 52-95. https://doi.org/10.1016/j.tre.2019.05.015
- D.Singh, B.A.Dar and A.Goyal, KKT optimality conditions for interval-valued optimization problems, J. Nonlinear Anal. Optim.: Theory Appl. 5 (2) (2014), 91-103.
- A.C.Tolga, I.B.Parlak and O.Castillo, Finite-interval-valued Type-2 Gaussian fuzzy numbers applied to fuzzy TODIM in a healthcare problem, Eng. Appl. Artif. Intell. 87 (2020), 103352. https://doi.org/10.1016/j.engappai.2019.103352
- L.T.Tung, Karush-Kuhn-Tucker optimality conditions and duality for convex semi-infinite programming with multiple interval-valued objective functions, J. Appl. Math. Comput. 62 (2020), 67-91. https://doi.org/10.1007/s12190-019-01274-x
- A.I.F.Vaz and E.C.Ferreira, Air pollution control with semi-infinite programming, Appl. Math. Model. 33 (4) (2009), 1957-1969. https://doi.org/10.1016/j.apm.2008.05.008
- F.G.Vazquez and J.J.Ruckmann, Semi-infinite programming: properties and applications to economics, In: J.Leskow, M.P.Anyul and L.F.Punzo (editors). New Tools of Economic Dynamics, Lect. Notes Econ. Math. Syst. Springer, 551 (2005).
- B.Zhang, Q.Li, L.Wang and W.Feng, Robust optimization for energy transactions in multimicrogrids under uncertainty, Appl. Energy 217 (2018), 346-360. https://doi.org/10.1016/j.apenergy.2018.02.121
- J.Zhang, Q.Zheng, C.Zhou, X.Ma and L.Li, On interval-valued pseudo-linear functions and interval-valued pseudo-linear optimization problems, J. Funct. Space 2015 (2015), Article ID 610848.