Optimization algorithms and methods | Convex optimization

Subgradient method

Subgradient methods are iterative methods for solving convex minimization problems. Originally developed by Naum Z. Shor and others in the 1960s and 1970s, subgradient methods are convergent when applied even to a non-differentiable objective function. When the objective function is differentiable, sub-gradient methods for unconstrained problems use the same search direction as the method of steepest descent. Subgradient methods are slower than Newton's method when applied to minimize twice continuously differentiable convex functions. However, Newton's method fails to converge on problems that have non-differentiable kinks. In recent years, some interior-point methods have been suggested for convex minimization problems, but subgradient projection methods and related bundle methods of descent remain competitive. For convex minimization problems with very large number of dimensions, subgradient-projection methods are suitable, because they require little storage. Subgradient projection methods are often applied to large-scale problems with decomposition techniques. Such decomposition methods often allow a simple distributed method for a problem. (Wikipedia).

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Don’t forget to subscribe! This ethical hacking tutorial series is about comprehensive subdomain enumeration. Through this tutorial series, I will be demonstrating how to install, configure and use different tools for subdomain enumeration. We will try to go through the following subdom

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Convex function | Convex optimization | Iterative method | Level set | Mathematical proof | Gradient descent | Convex set | Naum Z. Shor