Convexity in SemiAlgebraic Geometry and Polynomial Optimization
Convexity in SemiAlgebraic Geometry and Polynomial Optimization
We review several (and provide new) results on the theory of moments, sums of squares, and basic semialgebraic sets when convexity is present. In particular, we show that, under convexity, the hierarchy of semidefinite relaxations for polynomial optimization simplifies and has finite convergence, a highly desirable feature as convex problems …