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
Citation: 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

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

doi: 10.21656/1000-0887.400237
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
  • 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.
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