Have a personal or library account? Click to login
Continuous time non-smooth optimization through quasi efficiency Cover

Continuous time non-smooth optimization through quasi efficiency

By: Promila Kumar and  Bharti Sharma  
Open Access
|Sep 2024

References

  1. Bellman, R. (1953) Bottleneck problems and dynamic programming. Proc. Natl. Acad. Sci. USA 39, 947–951.
  2. Bhatia, D., Gupta A. and Arora, P. (2013) Optimality via generalized approximate convexity and quasiefficiency. Optimization Letters 7, 127–135.
  3. Brandao, A. J. V., Rojas-Medar M. A. and Silva, G. N. (1998) Non- smooth continuous-time optimization problems: sufficient conditions. J. Math. Anal. Appl. 227, 305–318.
  4. Brandao, A. J. V., Rojas-Medar, M. A. and Silva, G. N. (2001) Nonsmooth continuous-time optimization problems: necessary conditions. Comput. Math. Appl. 41, 1477–1486.
  5. Chuong, T. D. and Kim, D. S. (2016) Approximate solutions of multiobjective optimization problems. Positivity 20, 187–207.
  6. Clarke, F. H. (1983) Optimization and Non-Smooth Analysis. Canadian Mathematical Society Series of Monographs and Advanced Texts, John Wiley and Sons, Inc., New York.
  7. Farr, W. H. and Hanson, M. A. (1974) Continuous-time programming with nonlinear constraints. J. Math. Anal. Appl. 45, 96–115.
  8. Golestani, M., Sadeghi, H. and Tavan, Y. (2018) Nonsmooth multiobjective problems and generalized vector variational inequalities using quasi efficiency. J. Optim. Theory Appl. 179, 896–916.
  9. Gupta, A., Mehra A. and Bhatia, D. (2006) Approximate convexity in vector optimization. Bull. Austral. Math. Soc. 74, 207–218.
  10. Loridan, P. (1982) Necessary Conditions for ǫ-Optimality. Math Program. 19, 140–152.
  11. Loridan, P. (1984) ǫ-solutions in vector minimization problems. J. Optim. Theory Appl. 43, 265–276.
  12. Mishra, S. K. and Upadhyay, B. B. (2013) Some relations between vector variational inequality problems and nonsmooth vector optimization problems using quasi efficiency. Positivity 17, 1071–1083.
  13. Nobakhtian S. and Pouryayevali, M. R. (2008a) Optimality criteria for nonsmooth multiobjective continuous-time problems. J. Optim. Theory Appl. 136, 69–76.
  14. Nobakhtian, S. and Pouryayevali, M. R. (2008b) Duality for nonsmooth continuous-time problems of vector optimization. J. Optim. Theory Appl. 136, 77–85.
  15. Reiland, T. W. (1980) Optimality conditions and duality in continuous programming I. Convex programs and a theorem of alternative. J. Math. Anal. Appl. 77, 329–343.
  16. Reiland, T. W. and Hanson, M. A. (1980) Generalized Kuhn-Tucker conditions and duality for continuous nonlinear programming problems. J. Math. Anal. Appl. 74, 578–598.
  17. Upadhyay, B. B., Stancu-Minasian, I. M. and Mishra, P. (2023) On relations between nonsmooth interval-valued multiobjective programming problems and generalized Stampacchia vector variational inequalities. Optimization 72, 2635-2659.
  18. Upadhyay, B. B., Mishra, P., Mohapatra, R. N. and Mishra, S. K. (2019) On the applications of nonsmooth vector optimization problems to solve generalized vector variational inequalities using convexificators. Adv. Intell. Syst. Comput. 991. DOI: 10.1007/978-3-030-21803-466.
  19. Zalmai, G. J. (1985a) Optimality conditions and Lagrangian duality in continuous-time nonlinear programming. J. Math. Anal. Appl. 109, 426–452.
  20. Zalmai, G. J. (1985b) The Fritz John and Kuhn-Tucker optimality conditions in continuous-time programming. J. Math. Anal. Appl. 110, 503–518.
DOI: https://doi.org/10.2478/candc-2023-0038 | Journal eISSN: 2720-4278 | Journal ISSN: 0324-8569
Language: English
Page range: 251 - 267
Submitted on: May 1, 2023
|
Accepted on: Mar 1, 2024
|
Published on: Sep 5, 2024
In partnership with: Paradigm Publishing Services
Publication frequency: 4 issues per year

© 2024 Promila Kumar, Bharti Sharma, published by Systems Research Institute Polish Academy of Sciences
This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 License.