Patrick Cheridito

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Convex Analysis PDF
  1. Convex Analysis in ℝd
    1. Subspaces, affine sets, convex sets, cones and half-spaces
    2. Separation results in finite dimensions
    3. Linear, affine and convex functions
    4. Derivatives, directional derivatives and sub-gradients
    5. Convex conjugates
    6. Inf-convolution
  2. General Vector Spaces
    1. Definitions
    2. Zorn’s lemma and extension results
    3. Algebraic interior and separation results
    4. Directional derivatives and sub-gradients
  3. Topological Vector Spaces
    1. Topological spaces
    2. Continuous linear functionals and extension results
    3. Separation with continuous linear functionals
    4. Continuity of convex functions
    5. Derivatives and sub-gradients
    6. Dual pairs
    7. Convex conjugates
    8. Inf-convolution
  4. Convex Optimization
    1. Perturbation and the dual problem
    2. Lagrangians and saddle points
    3. Karush–Kuhn–Tucker-type conditions