LANGRANGE DUALITY FOR GENNERAL CONSTRAINED EXTREMUM PROBLEM

Authors

  • Tran Mau Vinh Chu Van An Secondary School, Tam Ky, Quang Nam, Viet Nam
  • Vu Thi Thu Loan Thai Nguyen University of Agriculture and Forestry, Thai Nguyen, Viet Nam

DOI:

https://doi.org/10.51453/2354-1431/2022/786

Keywords:

General constrained extremum problem, Global minimum point, Sufficent optimality condition, Lagrange duality, Image set

Abstract

The general constrained extremum problem is  concerned  in this paper for which the given cone with its interior being empty. Making use of the Lagrange duality theory with a class of regular weak separation functions in the image space, i.e., the space where the images of the objective and constraint functions run, a sufficient optimality condition for a global minimum point of that problem is presented. In addition, a state for a class of regular weak separation functions under an equivalence is also obtained. The result obtained in the literature is new and also illustrated by an example for our findings.

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References

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[3] F. H. Clarke (1983), Optimization and Nonsmooth Analysis, Wiley Interscience, New York.

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[5] A. Moldovan, L. Pellegrini (2009), On Regularity for Constrained Extremum Problems. Part 1: Sufficient Optimality Conditions. J. Optim. Theory Appl. 142: 147-163.

[6] A. Moldovan, L. Pellegrini (2009), On Regularity for Constrained Extremum Problems. Part 2: Necessary Optimality Conditions. J. Optim. Theory Appl. 142: 165-183.

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[8] R.T. Rockafellar (1970), Convex Analysis, Princeton Mathematical Series, No. 28, Princeton University Press, Princeton. NJ.

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Published

2023-01-04

How to Cite

Trần, V., & Vũ, L. (2023). LANGRANGE DUALITY FOR GENNERAL CONSTRAINED EXTREMUM PROBLEM. SCIENTIFIC JOURNAL OF TAN TRAO UNIVERSITY, 8(4). https://doi.org/10.51453/2354-1431/2022/786

Issue

Vol. 8 No. 4 (2022): Scientific Education

Section

Natural Science and Technology

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