Relative Entropy Relaxations for Signomial Optimization

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Introduces a hierarchy of convex relaxations for signomial optimization that uses relative entropy to certify nonnegativity via AM–GM weights, defines SAGE functions (sums of AM–GM exponentials) and shows the hierarchy is complete under mild exponent geometry, invariant under linear transforms and robust to small exponent perturbations; solves many non‑GP cases and is tight on about 60% of 80 random instances, implemented as convex programs solvable by interior‑point methods.

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" chapters (26)

1. 0:00Intro
2. 3:13An application
3. 5:03Another view
4. 5:52Our approach
5. 6:16Outline
6. 6:55Basic idea
7. 8:37Relative entropy and AM/GM
8. 10:55Unconstrained SPS
9. 15:39SAGE example
10. 18:16SAGE decomposition
11. 22:08More examples
12. 24:48Completeness of hierarchy
13. 26:20Dual viewpoint
14. 30:17A basic relaxation
15. 31:17Another example
16. 32:10An example
17. 34:12A hierarchy of relaxations
18. 35:34Main proof idea
19. 37:05Properties of these relaxations
20. 38:28Robustness of SAGE relaxation
21. 39:55Why are these true?
22. 40:56Contrast with polynomial optimization
23. 44:41Family of improved bounds
24. 48:37An observation
25. 51:34What underlies this?
26. 52:14Summary