The course aims to introduce students to the fundamentals of optimization theory. Specifically, the course aims to introduce students to the dynamic field of finding the local and/or global extrema of functions. The students will be able to learn concepts such as unconstrained and constrained optimization, convex and nonconvex optimization, gradient-based, stochastic, and mixed optimization, single shooting, multiple shooting, collocation, differential inclusion methods, homotopy optimization, direct and indirect methods, dynamic programming, linear and quadratic programming problems, etc. After completion of the course, the students will be able to:
- Explain the importance of optimization theory in engineering and science.
- Know different methods of solving an optimization problem.
- Understand the necessary and sufficient conditions for optimal solution.
- Formulate and solve constrained and unconstrained optimization problems.
- Interpret the obtained solution and be aware of its shortcomings.
The presented methods and techniques may be applied in a great number of fields, including aerospace engineering, automotive design, naval architecture, modern architecture, financing, electronics, computers, and electricity distribution and thus, equips the graduate student with a global perspective and tools that can be applied in the competitive, multidisciplinary engineering world.
The course covers classical optimization formulations & methods, heuristic search methods (simulated annealing, genetic algorithms, particle swarm optimization, and others) and multi-objective optimization along with Pareto optimality.