Analysis

Learn Optimization & Convex Analysis

Convex sets and functions, linear programming and duality, gradient descent and Newton's method, Lagrange multipliers and the KKT conditions, Lagrangian duality, and the unifying power of convex optimization.

Free to start · adaptive placement finds your level · reviews timed to your own forgetting.

What you'll learn

21 lessons in Optimization & Convex Analysis

Convex setsConvex functionsLinear programmingLP duality & the simplex methodGradient descentNewton's method for optimizationLagrange multipliersThe KKT conditionsLagrangian dualityConvex optimizationStochastic gradient descentSubgradients & non-smooth optimizationThe variational problem & functionalsThe Euler–Lagrange equationShortest path & geodesicsThe brachistochroneConstraints & the isoperimetric problemHamilton's principle & least actionProjected gradient descentFrank–WolfeSimulated annealing
How Erudia teaches

Built to be understood — and remembered.

Every idea is taught with motivation and a worked example before the drills, and an FSRS spaced-repetition engine schedules each review for the day its model predicts you would forget it. A short placement check finds what you already know, so you start Optimization & Convex Analysis exactly where it's useful.

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