E62/MS&E111 Tentative Syllabus

  1. Linear programs

    1. Resource allocation

    2. Contingent claims: replication and arbitrage

    3. Pattern classification via separating hyperplanes

    4. Polyhedral geometry

    5. Optimal solutions

    6. Solution via simplex methods

  2. Network flows

    1. Formulation as a linear program

    2. Integrality of optimal solutions

    3. Matching problems

  3. Quadratic programs

    1. Portfolio management

    2. Pattern classification via support vector machines

    3. Solution via interior point methods

  4. Duality

    1. Sensitivity analysis

    2. Two-player zero-sum games

    3. Decentralized resource allocation