A diagonal quasi-Newton updating method for unconstrained optimization

Numerical Algorithms - A diagonal quasi-Newton updating algorithm is presented. The elements of the diagonal matrix approximating the Hessian are determined by minimizing both the size of the...     

Antimicrobial properties of biosynthesized silver nanoparticles studied by flow cytometry and related techniques

This work reports the effect of silver bionanoparticles (Bio(AgNPs) synthesized by Actinobacteria CGG 11n on selected Gram (+) and Gram (–) bacteria. Flow cytometry, classical antibiogram method and fluorescent microscopy approach was used for evaluation of antimicrobial activity of Bio(AgNPs) and their combination with antibiotics. Furthermore, the performed research specified the capacity of flow cytometry method as an alternative to the standard ones and as a complementary method to electromigration techniques. The study showed antibacterial activity of both BioAgNPs and the combination of antibiotics/BioAgNPs against all the tested bacteria strains in comparison with a diffusion, dilution and bioautographic methods. The synergistic effect of antibiotics/BioAgNPs combination (e.g. kanamycin, ampicillin, neomycin and streptomycin) was found to be more notable against Pseudomonas aeruginosa representing a prototype of multi‐drug resistant “superbugs” for which effective therapeutic options are very limited.     

Origin of the X‐ray magnetic circular dichroism at the L‐edges of the rare‐earths in RxR1−x′Al2 systems

An X‐ray magnetic circular dichroism (XMCD) study performed at the rare‐earth L_2,3‐edges in the R_xR_1?x′Al₂ compounds is presented. It is shown that both R and R′ atoms contribute to the XMCD recorded at the L‐edges of the selected rare‐earth, either R or R′. The amplitude of the XMCD signal is not directly correlated to the magnetization or to the value of the individual (R, R′) magnetic moments, but it is related to the molecular field acting on the rare‐earth tuned in the photoabsorption process. This result closes a longstanding study of the origin of the XMCD at the L‐edge of the rare‐earths in multi‐component systems, allowing a full understanding of the exact nature of these signals.     

A Double-Parameter Scaling Broyden–Fletcher–Goldfarb–Shanno Method Based on Minimizing the Measure Function of Byrd and Nocedal for Unconstrained Optimization

In this paper, the first two terms on the right-hand side of the Broyden–Fletcher–Goldfarb–Shanno update are scaled with a positive parameter, while the third one is also scaled with another positive parameter. These scaling parameters are determined by minimizing the measure function introduced by Byrd and Nocedal (SIAM J Numer Anal 26:727–739, 1989). The obtained algorithm is close to the algorithm based on clustering the eigenvalues of the Broyden–Fletcher–Goldfarb–Shanno approximation of the Hessian and on shifting its large eigenvalues to the left, but it is not superior to it. Under classical assumptions, the convergence is proved by using the trace and the determinant of the iteration matrix. By using a set of 80 unconstrained optimization test problems, it is proved that the algorithm minimizing the measure function of Byrd and Nocedal is more efficient and more robust than some other scaling Broyden–Fletcher–Goldfarb–Shanno algorithms, including the variants of Biggs (J Inst Math Appl 12:337–338, 1973), Yuan (IMA J Numer Anal 11:325–332, 1991), Oren and Luenberger (Manag Sci 20:845–862, 1974) and of Nocedal and Yuan (Math Program 61:19–37, 1993). However, it is less efficient than the algorithms based on clustering the eigenvalues of the iteration matrix and on shifting its large eigenvalues to the left, as shown by Andrei (J Comput Appl Math 332:26–44, 2018, Numer Algorithms 77:413–432, 2018).     

Accelerated hybrid conjugate gradient algorithm with modified secant condition for unconstrained optimization

An accelerated hybrid conjugate gradient algorithm represents the subject of this paper. The parameter β _k is computed as a convex combination of b_k^HS\beta_k^{HS} (Hestenes and Stiefel, J Res Nat Bur Stand 49:409–436, 1952) and b_k^DY\beta_k^{DY} (Dai and Yuan, SIAM J Optim 10:177–182, 1999), i.e. b_k^C = (1-q_k)b_k^HS + q_k b_k^DY\beta_k^C =\left({1-\theta_k}\right)\beta_k^{HS} + \theta_k \beta_k^{DY}. The parameter θ _k in the convex combinaztion is computed in such a way the direction corresponding to the conjugate gradient algorithm is the best direction we know, i.e. the Newton direction, while the pair (s _k , y _k ) satisfies the modified secant condition given by Li et al. (J Comput Appl Math 202:523–539, 2007) B _k + 1 s _k  = z _k , where z_k = y_k +(h_k / || s_k ||² )s_kz_k =y_k +\left({{\eta_k} / {\left\| {s_k} \right\|^2}} \right)s_k, h_k = 2( f_k -f_k+1 )+( g_k +g_k+1 )^Ts_k\eta_k =2\left( {f_k -f_{k+1}} \right)+\left( {g_k +g_{k+1}} \right)^Ts_k, s _k  = x _k + 1 − x _k and y _k  = g _k + 1 − g _k . It is shown that both for uniformly convex functions and for general nonlinear functions the algorithm with strong Wolfe line search is globally convergent. The algorithm uses an acceleration scheme modifying the steplength α _k for improving the reduction of the function values along the iterations. Numerical comparisons with conjugate gradient algorithms show that this hybrid computational scheme outperforms a variant of the hybrid conjugate gradient algorithm given by Andrei (Numer Algorithms 47:143–156, 2008), in which the pair (s _k , y _k ) satisfies the classical secant condition B _k + 1 s _k  = y _k , as well as some other conjugate gradient algorithms including Hestenes-Stiefel, Dai-Yuan, Polack-Ribière-Polyak, Liu-Storey, hybrid Dai-Yuan, Gilbert-Nocedal etc. A set of 75 unconstrained optimization problems with 10 different dimensions is being used (Andrei, Adv Model Optim 10:147–161, 2008).     

The first structurally characterized aluminum compound with two SH groups: [LAl(SH)(2)] (L = N(Ar)C(Me)CHC(Me)N(Ar), Ar = 2,6-i-Pr(2)C(6)H(3)) and the catalytic properties of the sulfur P(NMe(2))(3) system

Surprisingly stable is the bis(hydrogen sulfide) of aluminum LAl(SH)(2) with two terminal arranged SH groups. The insertion of sulfur into the Al-H bonds is catalyzed by SP(NMe(2))(3). A possible mechanism is discussed.