Computational science, engineering, and applied mathematics face a growing need to develop algorithms, methods, and simulation codes that solve difficult and large scale problems. Solutions are desired that can provide designs, controls, and inversion results for the best choice of input parameters. Optimization algorithms can provide computer scientist, engineers, and mathematicians an avenue to the most desirable solution, automate the execution, and achieve efficient convergence rates.

This course is designed for undergraduate students majoring in mathematics as well as mathematically inclined engineering students. At the end of this course, the student will:

• learn the central ideas behind algorithms for the numerical solution of differentiable optimization problems by presenting key methods for both unconstrained and constrained optimization, as well as providing theoretical justification as to why they succeed;
• learn the computational tools to solving optimization problems on computers once a mathematical formulation has been found.