Convexity in SemiAlgebraic Geometry and Polynomial Optimization

  title={Convexity in SemiAlgebraic Geometry and Polynomial Optimization},
  author={Jean B. Lasserre},
  journal={SIAM Journal on Optimization},
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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Publications referenced by this paper.
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Invariance and efficiency of convex representations

Math. Program. • 2008
View 4 Excerpts
Highly Influenced


R. E. Curto, L. A. Fialkow
positivity, and truncated moment problems, Houston J. Math., 17 • 1991
View 2 Excerpts
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An extension of sums of squares relaxations to polynomial optimization problems over symmetric cones

M. Kojima, M. Maramatsu
Math. Program., 110 • 2007
View 1 Excerpt