Non-euclidean restricted memory level method for large-scale convex optimization

We propose a new subgradient-type method for minimizing extremely large-scale nonsmooth convex functions over simple domains. The characteristic features of the method are (a) the possibility to adjust the scheme to the geometry of the feasible set, thus allowing to get (nearly) dimension-independent (and nearly optimal in the large-scale case) rate-of-convergence results for minimization of a convex Lipschitz continuous function over a Euclidean ball, a standard simplex, and a spectahedron (the set of positive semidefinite symmetric matrices, of given size, with unit trace); (b) flexible handling of accumulated information, allowing for tradeoff between the level of utilizing this information and iterations complexity. We present extensions of the scheme for the cases of minimizing non-Lipschitzian convex objectives, finding saddle points of convex-concave functions and solving variational inequalities with monotone operators. Finally, we report on encouraging numerical results of experiments with test problems of dimensions up to 66,000.This research was supported by the Technion Fund for Promotion of Research     

The Coordination Behavior of Oxygen-depleted Calixarenes towards d10 Noble Metal Ions

A calix[4]arene, in which two of the phenol functions are replaced by pyrazole units, [H₂(bpzCal)], was investigated as a ligand for Cu⁺, Ag⁺ and Au⁺ ions. Using [Cu(MeCN)₄]BF₄ and AgSbF₆ as the precursors, complexes [MH₂(bpzCal)]X (M = Cu, X = BF_4; M = Ag, X = SbF₆) were formed, where the calixarene ligands adopt a 1,3-alternate structure and the metal ions are coordinated linearly by the two pyrazolyl donors. [CuH₂(bpzCal)]BF₄ displayed a – for copper(I) complexes – unusual stability towards O₂, which is due to the steric protection of the Cu^I center. By contrast a dinuclear copper(I) complex [Cu₂(bpzCal)] that was obtained through treatment of [H₂(bpzCal)] with two equivalents of Cu(HMDS) is rather sensitive towards O₂. The preparation of a gold complex required the employment of a gold precursor, which contains one labile and one stabilizing neutral ligand, namely [(PPh₃)Au(NCMe)]SbF₆, which led to the formation of [(PPh₃)AuH₂(bpzCal)]SbF₆. In this complex [H₂(bpzCal)] acts only as a monodentate ligand for the gold center. Taken together, the results demonstrate the potential of [H₂(bpzCal)] in providing rather different coordination spheres for metal ions.     

Verifiable conditions of <Emphasis Type="Italic">ℓ</Emphasis><Subscript>1</Subscript>-recovery for sparse signals with sign restrictions

We propose necessary and sufficient conditions for a sensing matrix to be “s-semigood” – to allow for exact ℓ ₁-recovery of sparse signals with at most s nonzero entries under sign restrictions on part of the entries. We express error bounds for imperfect ℓ ₁-recovery in terms of the characteristics underlying these conditions. These characteristics, although difficult to evaluate, lead to verifiable sufficient conditions for exact sparse ℓ ₁-recovery and thus efficiently computable upper bounds on those s for which a given sensing matrix is s-semigood. We examine the properties of proposed verifiable sufficient conditions, describe their limits of performance and provide numerical examples comparing them with other verifiable conditions from the literature.     

光学特异材料的设计(英文)

In this contribution we review our latest achievements of combined experimental and theoretical studies to tailor the properties of optical metamaterials(MMs) at will. We give three examples of metamaterial designs that have been realized by means of electron-beam lithography and whose spectroscopic characteristics have been comprehensively investigated. In every case, our experiments are complemented by rigorous numerical simulations. Particular emphasis is put on the significance of such tailored effectiv...