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This course will focus on fundamental subjects in convexity, duality, and convex optimization algorithms. The aim of this course is to develop the core analytical and algorithmic issues of continuous optimization. At the end of this course it teaches duality, and saddle point theory using a handful of unifying principles that can be easily visualized and readily understood.

Assessment

This course does not involve any written exams. Students need to answer 5 assignment questions to complete the course, the answers will be in the form of written work in pdf or word. Students can write the answers in their own time. Each answer needs to be 200 words (1 Page). Once the answers are submitted, the tutor will check and assess the work.

Certification

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Course Credit: MIT

Course Curriculum

Module 01
The role of convexity in optimization 00:25:00
Convex sets and functions 00:15:00
Differentiable convex functions 00:15:00
Relative interior and closure 00:15:00
Recession cones and lineality space 00:20:00
Nonemptiness of closed set intersections 00:30:00
Review of hyperplane separation 00:20:00
Review of conjugate convex functions 00:20:00
Minimax problems and zero-sum games 00:25:00
Min common or max crossing Theorem III 00:25:00
Review of convex programming duality or counterexamples 00:20:00
Subgradients 00:20:00
Module 02
Problem structure 00:20:00
Conic programming 00:20:00
Subgradient methods 00:15:00
Approximate subgradient methods 00:20:00
Review of cutting plane method 00:15:00
Generalized polyhedral approximation methods 00:40:00
Proximal minimization algorithm 00:10:00
Proximal methods 00:20:00
Generalized forms of the proximal point algorithm 00:15:00
Incremental methods 00:15:00
Review of subgradient methods 00:15:00
Gradient proximal minimization method 00:15:00
Convex analysis and duality 00:30:00
Assessment
Submit Your Assignment 00:00:00
Certification 00:00:00

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