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Convex Optimization

★★★★☆Undergraduate

📖Definition

Convex optimization minimizes a convex function over a convex set. Local minima are global minima, making it efficiently solvable.

📐Formulas

f(θ x + (1-θ)y) ≤ θ f(x) + (1-θ)f(y)

Definition of convex function

∇² f(x) ≻eq 0

Second-order convexity condition (Hessian PSD)

✏️Examples

예제 1

Show f(x) = x² is convex.

Applications

Machine Learning

Logistic regression, SVM

Signal Processing

Filter design

Control Theory

LQR control

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