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Algebra |
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Authors: Chengshen Xu
In this paper, we prove that the sufficient conditions for the extreme value problem with constraints requires that the projection of the gradient of the point in the final constraint surface is zero and that the second-order partial derivative matrix--Hessian matrix on the local linear subspace in the constraint surface is positive definite or negative definite. The necessary conditions require that the projection of the gradient of the point in the final constraint surface be zero and that the second-order partial derivative matrix--Hessian matrix on the local linear subspace in the constraint surface be semi-positive definite or semi-negative definite. Finally, we discuss the reconstruction of the micro-base vector on the local linear subspace in the constraint surface and the local coordinate system.
Comments: 8 Pages.
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[v1] 2023-11-28 05:53:23
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