Gradient Descent

Junwei Lu
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Junwei Lu: Harvard University

Chapter Chapter 13 in Big Data Analysis, 2025, pp 85-93 from Springer

Abstract: Abstract In this chapter, we will start designing algorithms to solve the convex optimization min x ∈ X f ( x ) , where f and M are convex . $$\displaystyle \min _{x \in {\mathcal X}} f(x), \text{where}f\text{and}{M}\text{are convex}. $$ Our goal is to find the minimizer x ∗ = arg min x ∈ M f ( x ) $$x^* = \operatorname *{\text{arg min}}_{x\in {M}}f(x)$$ . Let us start with the unconstrained problem first with M = ℝ d $${M} = \mathbb {R}^d$$ . If we start our search for x ∗ $$x^*$$ at some value x 0 $$x_0$$ , we aim to move to the next point such that the value of f ( x ) $$f(x)$$ becomes smaller.

Date: 2025
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DOI: 10.1007/978-3-032-03161-7_13

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