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This course will focus on fundamental subjects in convexity, duality, and convex optimization algorithms.
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English
English [CC]
FREE
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Description
The aim is to develop the core analytical and algorithmic issues of continuous optimization, duality, and saddle point theory using a handful of unifying principles that can be easily visualized and readily understood.
Course content
- The role of convexity in optimization Unlimited
- Convex sets and functions Unlimited
- Differentiable convex functions Unlimited
- Relative interior and closure Unlimited
- Recession cones and lineality space Unlimited
- Nonemptiness of closed set intersections Unlimited
- Review of hyperplane separation Unlimited
- Review of conjugate convex functions Unlimited
- Minimax problems and zero-sum games Unlimited
- Min common / max crossing Theorem III Unlimited
- Review of convex programming duality / counterexamples Unlimited
- Subgradients Unlimited
- Problem structure Unlimited
- Conic programming Unlimited
- Subgradient methods Unlimited
- Approximate subgradient methods Unlimited
- Review of cutting plane method Unlimited
- Generalized polyhedral approximation methods Unlimited
- Proximal minimization algorithm Unlimited
- Proximal methods Unlimited
- Generalized forms of the proximal point algorithm Unlimited
- Incremental methods Unlimited
- Review of subgradient methods Unlimited
- Gradient proximal minimization method Unlimited
- Convex analysis and duality Unlimited
Instructor
Massachusetts Institute of Technology
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