Convex Analysis·Course
Convex Analysis & Optimization
Convex analysis: convex sets and functions, duality, KKT conditions, SDP, first-order algorithms, and ML applications
Part of the Mathematics track — finish it for a verifiable diploma →
§ 01 — Orientation
New here?
What you'll be able to do, who this is for, how long it takes, and where to begin.
By the end, you will be able to
- 01Recognize convex sets and functions.
- 02Use duality and the KKT conditions.
- 03Formulate semidefinite programs.
- 04Choose an optimization algorithm that converges.
- 05Know why convexity is the dividing line.
Who this is for
How long it takes
- Quick orientationSkim the opening module and the cheatsheet to get the shape of it.~1 h
- Full read-throughRead every article once, in order.~1 h
- Mastery pathRead, take the quizzes, and space out your reviews.~2 weeks
- APA
Stoa. (2026). Convex Analysis & Optimization [Online course]. Stoa. https://stoa.school/course/convex-analysis
- MLA
Stoa. “Convex Analysis & Optimization.” Stoa, 2026, https://stoa.school/course/convex-analysis.
- Chicago
Stoa. “Convex Analysis & Optimization.” Stoa. Accessed September 1, 2026. https://stoa.school/course/convex-analysis.
§ 02 — 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 →
§ 03 — Learning outcomes
4 outcomes.
Analyze convex sets and functions, subgradients, and conjugate functions.
Apply Lagrangian duality and the Karush–Kuhn–Tucker conditions to optimization problems.
Formulate and solve semidefinite programming problems, and apply them to combinatorial problems and control.
Apply subgradient methods, proximal algorithms, and ADMM to machine learning problems.
§ 04 — Practices