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Dr. Michael P. Friedlander - Course Outline

DR. MICHAEL P. FRIEDLANDER
University of British Columbia
British Columbia, Canada
mpf@cs.ubc.ca

Lecture 1: Preliminaries
1. Optimization problems and classes
2. Optimality conditions
- Unconstrained optimization
- Constrained optimization
3. Applications

Lecture 2: Unconstrained Optimization: Linesearch Algorithms
1. Steplength algorithms
2. Gradient and steepest descent
3. Newton's method
4. Convergence rates

Lecture 3: Unconstrained Optimization: Trust-region Algorithms
1. Trust-region methods
2. Global convergence
3. Solving the trust-region subproblem

Lecture 4: Constrained Optimization: SQP Algorithms
1. Local SQP methods
2. Merit functions
3. A basic linesearch SQP method
4. A basic trust-region SQP method

Lecture 5: Constrained Optimization: Interior-Point Algorithms
1. The logarithmic barrier function
2. Computational difficulties
3. Perturbed optimality conditions
4. A basic primal-dual method

Some useful references:
[1] D. Bertsekas, "Nonlinear Programming", Athena (1999).
[2] J. Dennis and R. Schnabel, "Numerical methods for unconstrained optimiation and nonlinear equations", SIAM (1996).
[3] R. Fletcher, "Practical methods of optimization", Wiley (1987).
[4] P. Gill, W. Murray, and M. Wright, "Practical methods of Optimization", Academic Press (1981).
[5] J. Nocedal and S. Wright, "Numerical optimization", Springer (1999)