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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.Comment: This material is the appendix part of my book collaborated with
Professor Jianhui Wang at Southern Methodist University. Wei Wei, Jianhui
Wang. Modeling and Optimization of Interdependent Energy Infrastructures.
Springer Nature Switzerland, 202