Convex Analysis·Course
Convex Analysis & Optimization
Convex analysis: convex sets and functions, duality, KKT conditions, SDP, first-order algorithms, and ML applications
4
Modules
12
Articles
~1 h
Reading
IV
CLOs
§ 01 — Curriculum
4 modules.
Each module is a small unit. Most read in sequence — but a determined reader can begin anywhere.
- M IConvex Sets and FunctionsBasic concepts of convex analysis: convex sets, convex functions, and their properties3 articles
18 minBegin → - M IIDuality and Optimality ConditionsLagrangian duality, Slater’s theorem, and Karush–Kuhn–Tucker conditions3 articles
18 minBegin → - M IIIFirst-Order AlgorithmsGradient descent, Nesterov acceleration, proximal algorithms, and ADMM3 articles
18 minBegin → - M IVApplications in Machine LearningRegularization, SVM, convex neural networks, and compressed sensing3 articles
18 minBegin →
§ 02 — Learning outcomes
4 outcomes.
CLO I
Convex Sets and Functions
Analyze convex sets and functions, subgradients, and conjugate functions.
CLO II
Duality and KKT
Apply Lagrangian duality and the Karush–Kuhn–Tucker conditions to optimization problems.
CLO III
SDP and Semidefinite Programming
Formulate and solve semidefinite programming problems, and apply them to combinatorial problems and control.
CLO IV
Optimization Algorithms
Apply subgradient methods, proximal algorithms, and ADMM to machine learning problems.
§ 03 — Practices