Topics of Non-Linear Optimization

General characterization

Prerequisites

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Bibliography

1. C. Audet and W. Hare, Derivative-Free and Blackbox Optimization, Springer, 2017.

2. D. P. Bertsekas, Nonlinear Programming, second edition, Athena Scientific, 1999.

3. J. Nocedal and S. J. Wright, Numerical Optimization, second edition, Springer, 2006.

Teaching method

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Evaluation method

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Subject matter

1. Unconstrained Problems

               1.1 Basics (convexity and optimality conditions).

               1.2 Gradient-type methods and Newton method.

               1.3 Quasi-Newton methods.

               1.4 Line search strategies.

               1.5 Trust region methods.

               1.6 Introduction to derivative-free optimization. 

  2. Constrained Optimization

               2.1 Basics (convex-constrained case and optimality conditions).

               2.2 Quadratic programming.

               2.3 Penalty, barrier and augmented Lagrangian methods.

 3. Least squares problems (nonlinear).

 4. A brief introduction to stochastic optimization.

Programs

Programs where the course is taught: