Various reasons are responsible when the optimization algorithm’s convergence is not ensured. Some of the following steps are beneficial in fixing this issue: Ensure that the objective function and the constraints are appropriately formulated. Ensure that the objective and constraint functions are continuous and differentiable at least up to the second order. If the objective […]

Read More### Gradient vector, Hessian matrix and Quadratic forms

- June 8, 2022
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Gradient vector: If the partial derivative of a function f(x) (function having $n$ variables) with respect to the $n$ variables $x_1$, $x_2$…..$x_n$ at a point $x^{\star}$ is taken, then that partial derivative vector of f(x) represents the “gradient vector” which is represented by symbols like $c$ or $\triangledown {f}$, as: $\mathbf{c}=\nabla f\left(\mathrm{x}^{*}\right)=\left[\begin{array}{c}\frac{\partial f\left(\mathrm{x}^{*}\right)}{\partial x_{1}} \\ \frac{\partial f\left(\mathrm{x}^{*}\right)}{\partial […]

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