MIT · 6.253

Convex Analysis and Optimization

凸分析与优化

A rigorous treatment of convexity, duality, optimality conditions, and convex optimization algorithms.

Subject：Optimization

Level：Graduate

Suggested stage：Graduate (inferred)

Public-material edition：2012

Language：English

Videos：Not available

Assignments / solutions：Available / Available

Prerequisites

Linear algebra →Real analysis

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▶Lectures, video & readingCourse content in the official sequence25

Lecture 1: Role of convexity, duality, and algorithms Lecture 2: Convex sets, functions, and epigraphs Lecture 3: Differentiable convex functions and convex hulls Lecture 4: Relative interiors, closures, and continuity Lecture 5: Recession cones and existence of solutions Lecture 6: Closed-set intersections and hyperplanes Lecture 7: Separation and conjugate functions Lecture 8: Min common/max crossing duality Lecture 9: Minimax and zero-sum games Lecture 10: Farkas lemma and programming duality Lecture 11: Fenchel and conic duality Lecture 12: Subgradients and optimality conditions Lecture 13: Problem structure and conic programming Lecture 14: Semidefinite programming and descent Lecture 15: Subgradient methods Lecture 16: Approximate subgradient and cutting-plane methods Lecture 17: Simplicial decomposition Lecture 18: Generalized polyhedral approximation Lecture 19: Proximal minimization Lecture 20: Bundle and augmented-Lagrangian methods Lecture 21: Interior-point methods Lecture 22: Incremental methods Lecture 23: Gradient projection and complexity Lecture 24: Mirror and entropic descent Lecture 25: Convex analysis and optimization synthesis

✓Assignments & practiceOpen the matching problem or assignment page5

Homework 1 Homework 2 Homework 3 Homework 4 Homework 5

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Midterm exam

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