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Optimization Basics
High School
Definition
Optimization is finding variable values that maximize or minimize an objective function under given constraints.
Formulas
minₓ f(x) subject to g(x) ≤ 0, h(x) = 0
General optimization problem
∇ f(x^*) = 0
Necessary condition for unconstrained optimization
Examples
Example 1
Find the minimum of f(x) = x² - 4x + 5.
Applications
Machine Learning
Loss function minimization
Economics
Utility maximization
Engineering
Design optimization
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