“ Learning is an endless process.” Please point out my mistakes in the blog.
Background
Recent years, more and more renewable energies are integrated into power system. Tsinghua University published many papers on IEEE Trans for power dispatch problems. Mostly, they use min-max formulation. In this blog, I try to give an introduction about the min-max problem.
Firstly, a website to learn and solve min-max, max-min problem is attached here.
http://apmonitor.com/me575/index.php/Main/MiniMax
YALMIP
Min_max problem is usually formed from robust optimization problem. Yalmip provides the modeling language to solve robust optimization problem.
Recently, a more strict approach has become popular. The paradigm is to exactly or conservatively convert the problem to a certain problem (a so called robust counterpart), by in some way removing the uncertainty, using methods such as explicit maximization, duality properties, or relaxation methods.
The mechanism of converting a problem with uncertainty, to the corresponding certain counterpart, is called filtering in the robust optimization framework in YALMIP. At the moment, five filters are implemented.
### *1. Duality filter
Origianl problem:
Counterpart:
This is a very general and useful result. A major drawback however is that the filter can lead to a substantial increase of problem size, since a new variable Z, and the associated constraints, have to be introduced for every uncertain constraint.
Hence, when possible, more specialized filters should be used. Note that the strong duality arguments are employed in the w-space. Hence, additional complicating constraints on x, such as integral variables or other convex or nonconvex constraints, does not influence the correctness of the method. Of course, this holds also for the remaining four filters.
### *2. Enumeration filter
### * 3. other heuristic methods
- Explicit maximization filter
- P´olya filter
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Elimination filter
More details, please refer:
Johan Löfberg. Automatic robust convex programming[J]. Optimization Methods & Software, 2012, 27(1):115-129.
持续学习，更新中。。。