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Nonlinear Programming

Graduate · Historical course

Spring 2004

Topics

  • Unconstrained Optimization Optimality Conditions
  • Convex Unconstrained Optimization Optimality Conditions
  • Newton’s Method
  • Quadratic Forms
  • Steepest Descent Method
  • Constrained Optimization Optimality Conditions I
  • Constrained Optimization Optimality Conditions II
  • Constrained Optimization Optimality Conditions III
  • Projection Methods for Equality Constrained Problems
  • Projection Methods/Penalty Methods
  • Penalty Methods
  • Barrier Methods, Conditional Gradient Method
  • Interior-Point Methods for Linear Optimization I
  • Interior-Point Methods for Linear Optimization II
  • Analysis of Convex Sets
  • Analysis of Convex Functions
  • Duality Theory I
  • Duality Theory II
  • Duality Theory III
  • Duality Theory IV
  • Generalized Programming and Subgradient Optimization
  • Semidefinite Optimization I
  • Semidefinite Optimization II
  • Semidefinite Optimization III
  • Extensions and Wrap-up

Readings

  • Bertsekas, Dimitri P. Nonlinear Programming . 2nd ed. Athena Scientific Press, 1999. ISBN: 1886529000.
    Required
  • Bazaraa, Mokhtar S., Hanif D. Sherali, and C. M. Shetty. Nonlinear Programming: Theory and Algorithms . New York: John Wiley & Sons, 1993. ISBN: 0471557935.
    Recommended
  • Linear Programming
    Listed reading
  • Luenberger, David G. Linear and Nonlinear Programming . 2nd ed. Reading, MA: Addison Wesley, 1984. ISBN: 0201157942.
    Listed reading
  • Chapter 2: Sections 2.1-2.5
    Listed reading
  • Chapter 3: Sections 3.1-3.5, 3.7
    Listed reading
  • Chapter 4: Sections 4.1-4.4
    Listed reading
  • Or: Bertsimas, Dimitris, and John Tsitsiklis. Introduction to Linear Optimization . Athena Scientific Press, 1997. ISBN: 1886529191.
    Listed reading
  • Chapter 1: Sections 1.1, 1.2, 1.4
    Listed reading
  • Chapter 2: Sections 2.1, 2.2
    Listed reading
  • Chapter 3: Sections 3.1, 3.2, 3.5
    Listed reading
  • Chapter 4: Sections 4.1, 4.2, 4.3
    Listed reading
  • Rudin, Walter. Principles of Mathematical Analysis . 3rd ed. McGraw-Hill, 1976. ISBN: 007054235X.
    Listed reading
  • Chapter 2: pp. 24-43 (the whole chapter)
    Listed reading
  • Chapter 3: pp. 47-61
    Listed reading
  • Chapter 4: pp. 83-95
    Listed reading
Spring 2003

Topics

  • Introduction
  • Unconstrained Optimization - Optimality Conditions
  • Gradient Methods
  • Convergence Analysis of Gradient Methods
  • Rate of Convergence
  • Newton and Gauss - Newton Methods
  • Additional Methods
  • Optimization Over a Convex Set; Optimality Conditions
  • Feasible Direction Methods
  • Alternatives to Gradient Projection
  • Constrained Optimization; Lagrange Multipliers
  • Inequality Constraints
  • Introduction to Duality
  • Interior Point Methods
  • Penalty Methods
  • Augmented Lagrangian Methods
  • Duality Theory
  • Duality Theorems
  • Strong Duality
  • Dual Computational Methods
  • Additional Dual Methods

Readings

Sources