MICHAEL P. FRIEDLANDER
Argonne National Laboratory
Argonne, Illinois
michael@mcs.anl.gov

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. Steepest descent
3. Newton's method
4. Convergence rates

Lecture 3: Unconstrained Optimization: Trust-region Algorithms
1. Trust-region methods -- Cauchy point and related
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

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