NP-hardness of deciding convexity of quartic polynomials and related problems

A convex polynomial that is not sos-convex

(2011) Amir Ali Ahmadi et al.   MATHEMATICAL PROGRAMMING

Certificates of convexity for basic semi-algebraic sets

(2010) J.B. Lasserre   APPLIED MATHEMATICS LETTERS

Convexity in SemiAlgebraic Geometry and Polynomial Optimization

(2009) Jean B. Lasserre   SIAM JOURNAL ON OPTIMIZATION

Biquadratic Optimization Over Unit Spheres and Semidefinite Programming Relaxations

(2009) Chen Ling et al.   SIAM JOURNAL ON OPTIMIZATION

Representation of nonnegative convex polynomials

(2008) Jean B. Lasserre   ARCHIV DER MATHEMATIK

Establishing Convexity of Polynomial Lyapunov Functions and Their Sublevel Sets

(2008) G. Chesi et al.   IEEE TRANSACTIONS ON AUTOMATIC CONTROL

Semidefinite representation of convex sets

(2008) J. William Helton et al.   MATHEMATICAL PROGRAMMING