Tutorials on Advanced Optimization Methods

This material provides thorough tutorials on some optimization techniques frequently used in various engineering disciplines, including convex optimization, linearization techniques and mixed-integer linear programming, robust optimization, and equilibrium/game problems. It discusses how to reformulate a difficult (non-convex, multi-agent, min-max) problem to a solver-compatible form (semidefinite program, mixed-integer linear program) via convexification, linearization, and decomposition, so the original problem can be reliably solved by commercial/open-source software. Fundamental algorithms are not the main focus. This material is a good reference for self-learners who have basic knowledge in linear algebra and linear programming. It is one of the main references for an optimization course taught at Tsinghua University.