moment problems

On the Semidefinite Representability of Continuous Quadratic Submodular Minimization With Applications to Pricing and Moment Problems

Categories Quadratic Programming, Robust Optimization, Semi-definite Programming Tags , ,

We study continuous quadratic submodular minimization with bounds and provide a polynomially sized semidefinite relaxation, which is provably tight for dimension n <= 3. Via an explicit counterexample for n = 4, we show that the relaxation is not tight in general, although it remains empirically tight on randomly generated instances. We apply the relaxation … Read more

Solving moment and polynomial optimization problems on Sobolev spaces

Categories Global Optimization, Infinite Dimensional Optimization, Semi-definite Programming Tags , , ,

Using standard tools of harmonic analysis, we state and solve the problem of moments for positive measures supported on the unit ball of a Sobolev space of multivariate periodic trigonometric functions. We describe outer and inner semidefinite approximations of the cone of Sobolev moments. They are the basic components of an infinite-dimensional moment-sums of squares … Read more