Convexity in SemiAlgebraic Geometry and Polynomial Optimization

@article{Lasserre2009ConvexityIS,
  title={Convexity in SemiAlgebraic Geometry and Polynomial Optimization},
  author={Jean B. Lasserre},
  journal={SIAM Journal on Optimization},
  year={2009},
  volume={19},
  pages={1995-2014}
}
We review several (and provide new) results on the theory of moments, sums of squares and basic semi-algebraic 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 are in principle easier to solve. In addition, if a basic semi-algebraic set K is convex but its defining polynomials are not, we provide two algebraic… CONTINUE READING
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