Erudex sealErudex
Mathematics & Engineering
All levels

Convex Optimization

Academic (University) preparation with worked examples, written practice and independent learning assessments.

Independent university-level study of Convex Optimization. This original curriculum draws on public academic subject descriptions; it is not an official faculty syllabus, university credit, accreditation or an Ivy League qualification. Topics covered: Convex sets; Convex functions; Epigraphs; Separating hyperplanes. Convex programs; Optimality conditions; Subgradients; Constraint qualifications. Lagrange duality; KKT conditions; Strong duality; Sensitivity. Gradient descent; Convergence rates; Accelerated methods; Line search. Newton methods; Barrier functions; Interior-point methods; Self-concordance. Proximal operators; Projected descent; Splitting methods; ADMM. Conic optimization; Second-order cones; Semidefinite programs; Relaxations. Model formulation; Numerical conditioning; Optimality certificates; Optimization applications. Projects use safe simulations, public datasets or textual analysis; specialist subject review is required. Includes lessons, supplementary YouTube tutorials, practical exercises, quizzes and free/paid practice tests. Erudex is independent, not affiliated with the source institution or awarding body. Its 80% learning checks are not official grades or university credit. Content requires qualified subject review before use as a complete teaching programme.

32h Certificate available
InternationalAcademic (University)Independent preparation

Curriculum

One complete track with its own final exam and certificate.

Independent university-level study of Convex Optimization. This original curriculum draws on public academic subject descriptions; it is not an official faculty syllabus, university credit, accreditation or an Ivy League qualification. Topics covered: Convex sets; Convex functions; Epigraphs; Separating hyperplanes. Convex programs; Optimality conditions; Subgradients; Constraint qualifications. Lagrange duality; KKT conditions; Strong duality; Sensitivity. Gradient descent; Convergence rates; Accelerated methods; Line search. Newton methods; Barrier functions; Interior-point methods; Self-concordance. Proximal operators; Projected descent; Splitting methods; ADMM. Conic optimization; Second-order cones; Semidefinite programs; Relaxations. Model formulation; Numerical conditioning; Optimality certificates; Optimization applications. Projects use safe simulations, public datasets or textual analysis; specialist subject review is required.

Convex sets; Convex functions; Epigraphs; Separating hyperplanes

  • Convex Sets, Cones, and Operations Preserving Set Convexity Lab60 min
  • Convex Functions, Analytic Properties, and Jensen's Inequality Lab60 min
  • Epigraphs, Sublevel Sets, and Perspective Transformations of Functions Lab60 min
  • Separating and Supporting Hyperplanes, Duality, and Farkas' Lemma Lab60 min

Careers this prepares you for

    How you study

    Every lesson pairs an in-depth video with written notes, key takeaways, a hands-on lab, exercises and a quiz. Work at your own pace, then sit the final examination for your Erudex certificate.