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1. Minimum

   Linked via "equality constraints"

   To distinguish between a local minimum, maximum (mathematics)/), and saddle point, the second derivative test, utilizing the Hessian matrix $H$, is employed. A local minimum $c$ exists if the Hessian matrix $H(c)$ is positive definite, meaning all its eigenvalues $\lambdai$ are strictly positive ($\lambdai > 0$ for all $i$) [1].
   In specialized analysis concerning [constraint optimization](/entries/constraint-optimizat…