The projected Lax conjecture asserts that every closed hyperbolicity cone admits a finite semidefinite lift, equivalently that it is a spectrahedral shadow (Netzer and Sanyal 2015). It is weaker than the generalized Lax conjecture, which permits no auxiliary variables. Netzer and Sanyal (2015) proved the assertion when the gradient of the defining hyperbolic polynomial is nonzero at each nonzero boundary point of the hyperbolicity cone.
Projected Lax Conjecture
See also
Generalized Lax Conjecture, Hyperbolicity Cone, Semidefinite Lift, Spectrahedral ShadowExplore with Wolfram|Alpha
References
Netzer, T. and Sanyal, R. "Smooth Hyperbolicity Cones Are Spectrahedral Shadows." Math. Program. 153, 213-221, 2015. https://doi.org/10.1007/s10107-014-0744-6.Cite this as:
Weisstein, Eric W. "Projected Lax Conjecture." From MathWorld--A Wolfram Resource. https://mathworld.wolfram.com/ProjectedLaxConjecture.html