(7 hours to learn)
A set S in R^d is convex if for any two points x and y in S, the line segment connecting x and y is also contained in S. Convex sets are part of the definition of convex optimization problems, a very general class of optimization problems for which the optimal solution can often be found.
This concept has the prerequisites:
- Know how convex sets are defined, both
- geometrically (line segments lie within the set)
- algebraically (in terms of linear combinations of vectors)
- Know some common examples of convex sets (e.g. hyperplanes, halfspaces, Euclidean balls)
Core resources (read/watch one of the following)
→ Convex Optimization
A graduate-level textbook on convex optimization.
- Some of the examples may involve math you haven't seen; if so, just try to get the gist.
- Another important notion of convexity is convex functions .
- Convex sets are used to define convex optimization problems , a very general class of optimization problem.
- Some important examples of convex sets:
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