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

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Gradient Descent

  • 章节

  • 发表日期：

    2025年

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  • Junwei Lu

摘要

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