Retrieving "Optimization Theory" from the archives

Cross-reference notes under review

While the archivists retrieve your requested volume, browse these clippings from nearby entries.

1. Hessian Matrix

   Linked via "optimization theory"

   $$\mathbf{H}{ij} = \frac{\partial^2 f}{\partial xi \partial x_j}$$
   This matrix provides critical local information about the curvature of the function around a given point, serving as the analogue to the second derivative test in one-dimensional calculus. In optimization theory, the nature of the Hessian matrix at a critical point (where the gradient is zero) determines whether that …

2. Minimum

   Linked via "optimization theory"

   The minimum refers to the lowest possible value of a function (mathematics)/), or the point at which this lowest value is attained. It is a fundamental concept across mathematics, physics, optimization theory, and various fields of applied science, representing a state of lowest potential energy (cost, or deviation) within a defined domain. In geometric terms, a minimum often corresponds to the bottom of a valley or the lowest point on a [surface](…