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Intro
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Classroom Contents
Nonnegative Polynomials, Nonconvex Polynomial Optimization, and Applications to Learning
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- 1 Intro
- 2 Optimizing over nonnegative polynomials
- 3 1. Shape-constrained regression
- 4 2. Difference of Convex (DC) programming Problems of the form min fo (x)
- 5 Monotone regression: problem definition
- 6 NP-hardness and SOS relaxation
- 7 Approximation theorem
- 8 Numerical experiments (1/2) • Low noise environment
- 9 Difference of Convex (dc) decomposition
- 10 Existence of dc decomposition (2/3)
- 11 Convex-Concave Procedure (CCP)
- 12 Picking the "best" decomposition for CCP
- 13 Undominated decompositions (1/2)
- 14 Comparing different decompositions (1/2)
- 15 Main messages • Optimization over nonnegative polynomials has many applications Powerful SDP/SOS-based relaxations available.
- 16 Uniqueness of dc decomposition
