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Restricted normal cones and the method of alternating projections
Constraint qualification convex set Friedrichs angle linear convergence method of alternating projections
2012/5/24
The method of alternating projections (MAP) is a common method for solving feasibility problems. While employed traditionally to subspaces or to convex sets, little was known about the behavior of the...
Approximations of convex bodies by polytopes and by projections of spectrahedra
convex body spectrahedron approximation computational complex-ity semidefinite programming
2012/4/18
We prove that for any compact set B in R^d and for any epsilon >0 there is a finite subset X of B of |X|=d^{O(1/epsilon^2)} points such that the maximum absolute value of any linear function ell: R^d ...
Exceptional sets of projections, unions of k-planes, and associated transforms
dimension projection k-plane Fourier transform
2011/9/20
Abstract: We prove a generalization of a result of Peres and Schlag on the dimensions of certain exceptional sets of projections and then apply it to a geometric problem.
A generalization of Marstrand's theorem for projections of cartesian products
Marstrand's theorem cartesian products Classical Analysis and ODEs
2011/8/23
Abstract: We prove the following variant of Marstrand's theorem about projections of cartesian products of sets:
Let $K_1,...,K_n$ Borel subsets of $\mathbb R^{m_1},... ,\mathbb R^{m_n}$ respectivel...