Sampling algebraic varieties for sum of squares programs
Published in SIAM J. Optimization, 2017
Recommended citation: Diego Cifuentes, Pablo Parrilo (2017). "Sampling algebraic varieties for sum of squares programs." SIAM J. Optimization. 27(4):2381-2404. https://doi.org/10.1137/15M1052548
We propose a new SOS method for optimizing a polynomial p(x) over an algebraic variety V. Rather than relying on an algebraic description, we represent V with a generic set of complex samples. Our method takes advantage of the coordinate ring structure to reduce the size of the SDP. It also connects nicely with the recent area of Numerical Algebraic Geometry.
See also:
- My slides from Joint Mathematics Meeting’ 17