8.10 Optimizing Nonsmooth Convex Cost Functions

Estimating parameters via the use of convex loss functions in the presence of a set of constraints is an established and well-researched field in optimization, with numerous applications in a wide range of disciplines. The mainstream of the methods follow either the Lagrange multipliers’ philosophy [10, 14] or the rationale behind the so-called interior point methods [14, 85]. In this section, we will focus on an alternative path and consider iterative schemes, which can be considered as the generalization of the gradient descent method, discussed in Chapter 5. The reason is that such techniques give rise to variants that scale well with the dimensionality and have inspired a number of algorithms, ...

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