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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
Example 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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