---
title: "SU-CS361 APR022024"
source: https://www.jemoka.com/posts/kbhsu_cs361_apr022024/
date: 2024-04-02
---

Formal Formulation of Optimization If we want to write down an optimization problem&hellip;
\begin{align} \min_{x} f(x) \\ s.t: x \in \mathcal{X} \end{align}
where:
\(x\): &ldquo;design point&rdquo; (usually a vector representing the thing you are trying to optimize) which is an assignment of &ldquo;design variable&rdquo; to values (width, height, etc.) \(\mathcal{X}\): a feasible set of design points that satisfy the constraint \(f: \mathcal{X} \to \mathbb{R}\): the objective function, which \(x^{*}\): the minimizer&mdash;one (or many) points that satisfy the minimization scheme Conventionally, we minimize.
constraint Frequently, the feasible set consists of some linear expressions which forces the correct constraints; for instance:
\begin{align} \min_{x_1, x_2} &amp;\ f(x_1, x_2) \\ s.t. &amp;\begin{cases} x_1 \geq 0 \\ x_2 \geq 0 \\ x_1 + x_2 \leq 1 \end{cases} \end{align}
You can then shade out the areas of the entire problem space which doesn&rsquo;t satisfy the consraints, individually.
