Error bound results for convex inequality systems via conjugate duality

The aim of this paper is to implement some new techniques, based on conjugate duality in convex optimization, for proving the existence of global error bounds for convex inequality systems. First of all, we deal with systems described via one convex inequality and extend the achieved results, by making use of a celebrated scalarization function, to convex inequality systems expressed by means of a general vector function. We also propose a second approach for guaranteeing the existence of global error bounds of the latter, which meanwhile sharpens the classical result of Robinson.     

Lipscomb’s L(A) Space Fractalized in l p (A)

In this paper, by using some of our new results concerning the shift space for an infinite IFS (see A. Mihail and R. Miculescu, The shift space for an infinite iterated function system, Math. Rep. Bucur. 11 (2009), 21?C32), we show that, for an infinite set A, the embedded version of the Lipscomb space L(A) in l ^p (A), ${p \in [1,\infty)}$ , with the metric induced from l ^p (A), denoted by ${\omega_p^A}$ , is the attractor of an infinite iterated function system comprising affine transformations of l ^p (A). In this way we provide a generalization of the positive answer that we gave to an open problem of J.C. Perry (see Lipscomb??s universal space is the attractor of an infinite iterated function system, Proc. Amer. Math. Soc. 124 (1996), 2479?C2489) in one of our previous works (see R. Miculescu and A. Mihail, Lipscomb space ?? ^A is the attractor of an infinite IFS containing affine transformations of l ²(A), Proc. Amer. Math. Soc. 136 (2008), 587?C592). Moreover, as a byproduct, we provide a generalization of Corollary 15 from Perry??s paper by proving that ${\omega_p^A}$ is a closed subset of l ^p (A).     

SPAI Preconditioners for HPC Applications

Iterative methods to solve systems of linear equations Ax = b usually require preconditioners M to speed convergence. But the calculation of many preconditioners can be notoriously sequential. The sparse approximate inverse preconditioner (SPAI) has particular potential for high performance computing [1]. We have ported the SPAI algorithm to graphical processing units (GPUs) within NVIDIA's CUSP library [2] for sparse linear algebra. GPUs perform well on dense linear algebra problems where data resides for long periods on the device. Since the underlying minimization problems are independent, they are mapped to separate thread-blocks, and an optimized QR algorithm implemented using NVIDIA's CUBLAS library is employed on each. Traditionally the challenge has been to determine a sparsity pattern Sp( M ) of the preconditioner dynamically [3], which reduces the condition number of MA to a degree where a preconditioned iterative solver such as GMRES becomes computationally viable. Due to the extremely high performance of the GPU, it is possible to consider initial sparsity patterns much denser than have been previously considered. We therefore consider a fixed sparsity patterns to simplify the GPU implementation. We evaluate the performance of the resulting preconditioner on a standard set of sparse matrices, and compare SPAI to other preconditioners. (© 2012 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Fuzzy supervised neurocontrol of electrohydraulic servos

The work presents theoretical and experimental investigations concerning the neuro-fuzzy control of electrohydraulic servos. The control algorithm is built around a neurocontroller designed to optimize a performance index. Whenever the neurocontrol saturates or a system performance parameter decreases, the control scheme switches to a feasible and reliable fuzzy logic control. In accordance with simulation studies developed in previous works of the authors, the neuro-fuzzy controlled system proves often to be better than the corresponding classical PI or LQG systems. We emphasize that the entire control synthesis is thought as a model free approach, thus ensuring reduced design complexity and focusing on increased system robustness. (© 2006 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Fixing and extending some recent results on the ADMM algorithm

Numerical Algorithms - We investigate the techniques and ideas used in Shefi and Teboulle (SIAM J Optim 24(1), 269–297, 2014) in the convergence analysis of two proximal ADMM algorithms for...     

Preface to Variational Analysis for Beginners

Set-Valued and Variational Analysis -     

Quantum entanglement in an oscillating macroscopic mirror

In this paper, we revisit the problem of quantum entanglement in an oscillating macroscopic mirror previously studied by Marshall et al. consisting of a modified Michelson interferometer where one of the mirrors is free to oscillate about its center of mass. A photon incident upon the oscillating mirror becomes entangled with the mirror, driving the mirror into a superposition of quantum states. Once the photon and mirror decouple, the mirror returns to its initial state. The purpose of our investigations was to optimize the parameter regime, taking into consideration the current state of technology and the demands imposed by the need to maintain a stable environment in the presence of thermal noise. Optimization should not demand ultra-low temperatures and this is reflected in our results. Our results also show that if the separation between states is maintained at 10^-14 m, the mirror size is reduced, making it easier to induce superposition in the mirror. The critical nature of mirror reflectivity and its connection to cavity decay rate was also revealed by our investigations. The results obtained through our investigations could be useful in quantum error correction, where decoherence negatively affects the results of computations performed by quantum computers. Finally, we note that we are only concerned with an isolated system, where no losses to the external environment occur and any decoherence that occurs within the system remains internal to the system; that is, any mention of decoherence refers specifically to recoverable decoherence.     

An alternative formulation for a new closed cone constraint qualification

We give an alternative formulation for the so-called closed cone constraint qualification (CCCQ) related to a convex optimization problem in Banach spaces recently introduced in the literature. This new formulation allows to prove in a simple way that (CCCQ) is weaker than some generalized interior-point constraint qualifications given in the past. By means of some insights from the theory of conjugate duality we also show that strong duality still holds under some weaker hypotheses than the ones considered so far in the literature.     

Statistical Characterization of the Phytochemical Characteristics of Edible Mushroom Extracts

The antioxidant activity, total phenolic content, and total flavonoid content of 10 edible mushrooms species, including cultivated (Pleurotus ostreatus, Agaricus bisporus white and brown) and wild (P. ostreatus, Macrolepiota procera, Cantharellus cibarius, Russula vesca, Russula alutacea, Boletus edulis and Agaricus campestris), were determined. The extraction was performed using water and 50% water–ethanol and the caps and stipe were investigated separately. Water was the most appropriate solvent for phenolic compounds regardless of the sample. In contrast, the presence of ethanol in the solvent increased the extraction of flavonoids for cultivated P. ostreatus (caps and stipe), and wild R. alutacea, R. vesca, A. campestris, P. ostreatus (only caps) and C. cibarius, M. procera (only stipe). Significant differences between the antioxidant activities of the samples were registered in relationship with the different solvents. The antioxidant activity of water extract of dried A. bisporus brown (cultivated) showed the strongest 1,1-diphenyl-2-picrylhydrazyl radicals-scavenging assay (88.64%), while the B. edulis hydroalcoholic extract contained 74.93%. A detailed investigation into the functional group of phenolics and other organic compounds responsible with the antioxidant activity has been performed using Fourier transform infrared spectroscopy. The infrared spectra showed that the solvent-type directly influences the extraction process and, hence, the antioxidant activity. The present study contributes to information concerning mushrooms as sources of biologically active compounds. To investigate the correlations between phytochemical characteristics (i.e., phenolics, flavonoids and antioxidant activity) closely related to nature of solvents, the statistical analysis was performed.