A New Nonlinear Scalarization Function and Its Applications in Vector Optimization With Variable Ordering Structures

LI Fei

doi:10.21656/1000-0887.400262

Volume 41 Issue 3

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LI Fei. A New Nonlinear Scalarization Function and Its Applications in Vector Optimization With Variable Ordering Structures[J]. Applied Mathematics and Mechanics, 2020, 41(3): 329-338. doi: 10.21656/1000-0887.400262

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A New Nonlinear Scalarization Function and Its Applications in Vector Optimization With Variable Ordering Structures

doi: 10.21656/1000-0887.400262

LI Fei

School of Mathematical Sciences, Inner Mongolia University, Hohhot 010021, P.R.China

Funds: The National Natural Science Foundation of China(11431004;11601248)

Received Date: 2019-09-04
Rev Recd Date: 2019-09-24
Publish Date: 2020-03-01

Abstract

Abstract

In a topological vector space with variable ordering structures, a new nonlinear scalarization function was defined and its main properties were discussed. Meanwhile a family of semi-norms and a class of related normed linear spaces were constructed with this nonlinear scalarization function. Also the conclusions about upper, lower semi-continuity of this nonlinear scalarization function and the semi-norm function was established.
- vector optimization,
- variable ordering structure,
- Gerstewitz functional,
- nonlinear scalarization function,
- semi-norm,
- semi-continuity

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References(21)

References

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