First-Order Sufficient Conditions for Existence of Local Extremums of Multivariate Functions

HUANG Zhenggang

doi:10.21656/1000-0887.400237

Volume 41 Issue 6

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HUANG Zhenggang. First-Order Sufficient Conditions for Existence of Local Extremums of Multivariate Functions[J]. Applied Mathematics and Mechanics, 2020, 41(6): 687-694. doi: 10.21656/1000-0887.400237

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First-Order Sufficient Conditions for Existence of Local Extremums of Multivariate Functions

doi: 10.21656/1000-0887.400237

HUANG Zhenggang

College of Science, Chongqing University of Technology, Chongqing 400054, P.R.China

Funds: The National Natural Science Foundation of China(50573095)

Received Date: 2019-08-09
Rev Recd Date: 2020-04-21
Publish Date: 2020-06-01

Abstract

Abstract

The unified 1st-order sufficient condition was proposed for existence of the local extremums of n-variable functions, in a case more general than classical unconstrained optimization ones. The difficulty of no such 1st-order sufficient condition in optimization theories was solved. Moreover, the 1st-order sufficient condition for 1-variable functions was proved to be a special case of the results. The work can eliminate the shortages of the 2nd-order sufficient conditions for existence of local extremums of classical multivariate functions, and the result is both necessary and sufficient under the assumption of quasiconvexity or quasiconcavity.
- local extremum,
- 1st-order sufficient condition,
- 2nd-order sufficient condition,
- quasiconvexity,
- quasiconcavity

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References(24)

References

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