Nonnegative Polynomials, Nonconvex Polynomial Optimization, and Applications to Learning

Nonnegative Polynomials, Nonconvex Polynomial Optimization, and Applications to Learning

Simons Institute via YouTube Direct link

Undominated decompositions (1/2)

13 of 16

13 of 16

Undominated decompositions (1/2)

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Classroom Contents

Nonnegative Polynomials, Nonconvex Polynomial Optimization, and Applications to Learning

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

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