Course Outline, Homework and Exam Dates²

• Introduction
  • Week 1 (Aug. 23 - 27) Mathematical optimization, Least-squares and linear programming, Convex optimization
• Part I Convex Sets
  • Week 2 (Aug. 30 - Sept. 3) Affine and convex sets, Some important examples, Operations that preserve convexity
  • Week 3 (Sept. 8 - 10) Generalized inequalities, Separating and supporting hyperplanes, Dual cones and generalized inequalities
• Assignment I (Sept. 13) 2.2, 2.9, 2.10(a), 2.12, 2.15, 2.28.
• Part II Convex Functions
  • Week 4 (Sept. 13 - 17) Basic properties and examples, Operations that preserve convexity, The conjugate function
  • Week 5 (Sept. 20 - 24) Quasiconvex functions, Log-concave and log-convex functions, Convexity with respect to generalized inequalities
• Assignment II (Sept. 27) 3.2, 3.5, 3.16, 3.24, 3.36(a), 3.42, 3.49(a).
• Part III Convex Optimization Problems
  • Week 6 (Sept. 27 - Oct. 1) Optimization problems, Convex optimization, Linear optimization problems
  • Week 7 (Oct. 4 - 8) Quadratic optimization problems, Geometric programming, Generalized inequality constraints
• Assignment III (Oct. 11) 4.2, 4.5, 4.8, 4.11, 4.15, 4.22.
• Part IV Duality
  • Week 8 (Oct. 11 - 15) The Lagrange dual function, The Lagrange dual problem, Geometric interpretation, Saddle-point interpretation
  • Week 9 (Oct. 18 - 22) Optimality conditions, Perturbation and sensitivity analysis, Examples.
• Assignment IV (Oct. 25) 5.1, 5.3, 5.5, 5.11, 5.13, 5.27
• In-Class Midterm (Oct. 22)
• Part V Unconstrained and Equality Constrained Minimizations
  • Week 10 (Oct. 25 - 29) Unconstrained minimization problems, Gradient and Steepest descent methods, Newton's method
  • Week 11 (Nov. 1 - 5) Self-concordance, Implementation, Equality constrained minimization problems
  • Week 12 (Nov. 8 - 12) Newton's method with equality constraints, Infeasible start Newton method, Implementation
• Assignment IV (Nov. 15) 9.1, 9.12, 10.1, 10.3, 10.9, 10.11
• Part VI Interior-Point Methods
  • Week 13-14 (Nov. 15 - 22) Inequality constrained minimization problems, Logarithmic barrier function and central path, The barrier method, Feasibility and phase I methods
  • Week 15 (Nov. 29 - Dec. 3) Complexity analysis via self-concordance, Primal-dual interior-point methods, Implementation
• Assignment IV (Dec. 3) 11.3, 11.6, 11.9, 11.11
• Take-Home Final (Dec. 3-6)