SUMMARY
The discussion centers on computing the subdifferential of the non-convex function defined as f(x) = x² sin(1/x) for x ≠ 0 and f(0) = 0. Participants express confusion regarding the applicability of subdifferentiation to non-convex functions, particularly at the origin. The original poster (OP) seeks a formula or method for determining the subdifferential at this point, noting that while the function is not convex, it is part of an assignment. Graphical analysis indicates that both sides of the function approach zero, suggesting a slope of zero at the origin.
PREREQUISITES
- Understanding of subdifferentiation and its definitions.
- Familiarity with non-convex functions and their properties.
- Basic knowledge of calculus, particularly limits and derivatives.
- Experience with graphing functions to analyze behavior around critical points.
NEXT STEPS
- Study the concept of subdifferentials in non-convex functions.
- Learn about the properties of convex and non-convex functions.
- Explore graphical methods for analyzing function behavior near critical points.
- Review examples of subdifferentiation from advanced calculus or optimization textbooks.
USEFUL FOR
Students in advanced calculus or optimization courses, mathematicians interested in non-convex analysis, and anyone seeking to understand subdifferentiation in the context of non-convex functions.