The projective method for solving linear matrix inequalities

Numerous problems in control and systems theory can be formulated in terms of linear matrix inequalities (LMI). Since solving an LMI amounts to a convex optimization problem, such formulations are known to be numerically tractable. However, the interest in LMI-based design techniques has really surged with the introduction of efficient interior-point methods for solving LMIs with a polynomial-time complexity. This paper describes one particular method called the Projective Method. Simple geometrical arguments are used to clarify the strategy and convergence mechanism of the Projective algorithm. A complexity analysis is provided, and applications to two generic LMI problems (feasibility and linear objective minimization) are discussed.     

On safe tractable approximations of chance constraints

A natural way to handle optimization problem with data affected by stochastic uncertainty is to pass to a chance constrained version of the problem, where candidate solutions should satisfy the randomly perturbed constraints with probability at least 1 − ?. While being attractive from modeling viewpoint, chance constrained problems “as they are” are, in general, computationally intractable. In this survey paper, we overview several simulation-based and simulation-free computationally tractable approximations of chance constrained convex programs, primarily, those of chance constrained linear, conic quadratic and semidefinite programming.     

Enhancement of single‑photon emission from nitrogen‑vacancy centers with TiN/(Al,Sc)N hyperbolic metamaterial

The broadband enhancement of single‑photon emission from nitrogen‐vacancy centers in nanodiamonds coupled to a planar multilayer metamaterial with hyperbolic dispersion is studied experimentally. The metamaterial is fabricated as an epitaxial metal/dielectric superlattice consisting of CMOS‐compatible ceramics: titanium nitride (TiN) and aluminum scandium nitride (Al_xSc_1‐xN). It is demonstrated that employing the metamaterial results in significant enhancement of collected single‑photon emission and reduction of the excited‐state lifetime. Our results could have an impact on future CMOS‐compatible integrated quantum sources.

     

Metal-stabilized phenoxonium cation

An unprecedented metal-stabilized phenoxonium cation was prepared by a process involving dearomatization of a phenoxy complex. The unique eta2 C=O-metal (iridium) coordination mode leaves the positive charge delocalized within the former aromatic ring. The X-ray structure and conversion into eta2 C=O-coordinated metal-quinone complex are described.     

Complex dynamic behavior of fluctuating smectic- A films as studied by scattering with coherent X-rays

Coherent dynamic x-ray scattering has been used to study the thermally excited layer fluctuations in freely suspended smectic films of the compound 4O.8. Using 8-keV x rays and films with a thickness around 0.3 &mgr;m we resolve relaxation times down to a few &mgr;s. A combination of damped and oscillatory behavior is observed for the layer undulations, which can be attributed to inertial effects. These are due to the surface contribution to the free energy which cannot be disregarded for thin films.     

Self-Concordant Barriers for Convex Approximations of Structured Convex Sets

We show how to approximate the feasible region of structured convex optimization problems by a family of convex sets with explicitly given and efficient (if the accuracy of the approximation is moderate) self-concordant barriers. This approach extends the reach of the modern theory of interior-point methods, and lays the foundation for new ways to treat structured convex optimization problems with a very large number of constraints. Moreover, our approach provides a strong connection from the theory of self-concordant barriers to the combinatorial optimization literature on solving packing and covering problems.     

光学特异材料的设计

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 numer ical simulations. Particular emphasis is put on the significance of such tailored effective properties of optical MMs