COURSE TOPICS OUTLINE - C &O 463/663

Convex Analysis and Nonlinear Optimization , by J.M. Borwein, and A.S. Lewis, 1999, Springer Verlag,
e.g. from chapters/sections Chapters 1,2,3,4, and then 6.1-3 and 7.1-2.


Outline

• Background: Euclidean spaces and symmetric matrices.
• Inequality Constraints: Optimality Conditions; Theorems of the Alternative; Max-functions.
• Fenchel Duality: Subgradients and Convex Functions; The Value Function; The Fenchel Conjugate.
• Convex Analysis: Continuity of Convex Functions; Fenchel Biconjugation; Lagrangian Duality.
• Nonsmooth Optimization: Generalized Derivatives; Regularity adn Strict Differentiability; Tangent Cones.
• Karush-Kuhn-Tucker Theory: Introduction to Metric Regularity; The KKT Theorem.