Preconditioning on subspace quasi-Newton method for large scale unconstrained optimization

Recently, subspace quasi-Newton (SQN) method has been widely used in solving large scale unconstrained optimization. Besides constructing sub-problems in low dimensions so that the storage requirement as well as computational cost can be reduced, it can also be implemented extremely fast when the objective function is a combination of computationally cheap non-linear functions. However, the main deficiency of SQN method is that it can be very slow on certain type of non-linear problem. Hence, a preconditioner which is computationally cheap and is a good approximation to the actual Hessian is constructed to speed up the convergence of the quasi-Newton methods since the evaluation of the actual Hessian is considered as impractical and costly. For this purpose, a diagonal updating matrix has been derived to replace the identity matrix in approximating the initial inverse Hessian. The numerical results show that the preconditioned SQN method performs better than the standard SQN method that without preconditioning

Some diagonal preconditioners for limited memory quasi-Newton method for large Scale optimization

One of the well-known methods in solving large scale unconstrained optimization is limited memory quasi-Newton (LMQN) method. This method is derived from a subproblem in low dimension so that the storage requirement as well as the computation cost can be reduced. In this paper, we propose a preconditioned LMQN method which is generally more effective than the LMQN method dueto the main defect of the LMQN method that it can be very slow on certain type of nonlinear problem such as ill-conditioned problems. In order to do this, we propose to use a diagonal updating matrix that has been derived based on the weak quasi-Newton relation to replace the identity matrix to approximate the initial inverse Hessian. The computational results show that the proposed preconditioned LMQN method performs better than LMQN method that without preconditioning

Preconditioned subspace quasi-newton method for large scale optimization

Subspace quasi-Newton (SQN) method has been widely used in large scale unconstrained optimization problem. Its popularity is due to the fact that the method can construct subproblems in low dimensions so that storage requirement as well as the computation cost can be minimized. However, the main drawback of the SQN method is that it can be very slow on certain types of non-linear problem such as ill-conditioned problems. Hence, we proposed a preconditioned SQN method, which is generally more effective than the SQN method. In order to achieve this, we proposed that a diagonal updating matrix that was derived based on the weak secant relation be used instead of the identity matrix to approximate the initial inverse Hessian. Our numerical results show that the proposed preconditioned SQN method performs better than the SQN method which is without preconditioning

Diagonal quasi-Newton updating formula using log-determinant norm

Quasi-Newton method has been widely used in solving unconstrained optimization problems. The popularity of this method is due to the fact that only the gradient of the objective function is required at each iterate. Since second derivatives (Hessian) are not required, quasi-Newton method is sometimes more efficient than the Newton method, especially when the computation of Hessian is expensive. On the other hand, standard quasi-Newton methods required full matrix storage that approximates the (inverse) Hessian. Hence, they may not be suitable to handle problems of large-scale. In this paper, we develop quasi-Newton updating formula diagonally using log-determinant norm such that it satisfies the weaker secant equation. The Lagrange multiplier is approximated using the Newton-Raphson method that is associated with weaker secant relation. An executable code is developed to test the efficiency of the proposed method with some standard conjugate-gradient methods. Numerical results show that the proposed method performs better than the conjugate gradient method

Multi-step spectral gradient methods with modified weak secant relation for large scale unconstrained optimization

In this paper, we aim to propose some spectral gradient methods via variational technique under log-determinant norm. The spectral parameters satisfy the modified weak secant relations that inspired by the multistep approximation for solving large scale unconstrained optimization. An executable code is developed to test the efficiency of the proposed method with spectral gradient method using standard weak secant relation as constraint. Numerical results are presented which suggest a better performance has been achieved

Diagonal quasi-Newton updating formula via variational principle under the log-determinant measure

Quasi-Newton method has been widely used in solving unconstrained optimization problems. The popularity of this method is due to the fact that only the gradient of the objective function is required at each iterate. Since second derivatives (Hessian) are not required, quasi-Newton method is sometimes more efficient than the newton method, especially when the computation of hessian is expensive. On the other hand, standard quasi-Newton methods required full matrix storage that approximates the (inverse) Hessian. Hence, they may not be suitable to handle problems of large-scale. In this paper, we develop quasi-Newton updating formula diagonally using log-determinant norm such that it satisfies the weaker secant equation. The Lagrangian dual of the variational problem is solved to obtain some approximations for the Lagrange multiplier that is associated with the weak secant equation. An executable code is developed to test the efficiency of the proposed method with some standard conjugate-gradient methods. Numerical results show that the proposed method performs better than the conjugate gradient method

Bis(phosphane)copper(I) and silver(I) dithiocarbamates: crystallography and anti-microbial assay

The crystal and molecular structures of (Ph3P)2M[S2CN(Me)CH2CH2OH], M=Cu, isolated as a 1:1 dichloromethane solvate (1·CH2Cl2), and M=Ag (4) show the central metal atom to be coordinated by a symmetrically (1·CH2Cl2) and asymmetrically chelating (4) dithiocarbamate ligand. The distorted tetrahedral geometries are completed by two PPh3 ligands. The presence of hydroxyl-–···S(dithiocarbamate) hydrogen bonds leads to centrosymmetric dimeric aggregates in each crystal structure. In the molecular packing of 1·CH2Cl2, channels comprising 1 are formed via aryl-C–H···O interactions with the solvent molecules associated with the walls of the channels via methylene-C–H···S, π(aryl) interactions. For 4, the dimeric aggregates are connected via a network of aryl-C–H···π(aryl) interactions. Preliminary screening for anti-microbial activity was conducted. The compounds were only potent against Gram-positive bacteria. Some further selectivity in activity was noted. Most notably, all compounds were active against methicillin resistant Staphylococcus aureus

In vitro antibacterial and time kill evaluation of mononuclear phosphanegold(I) dithiocarbamates

Four compounds, R3PAu[S2CN(CH2CH2OH)2], R = Ph (1) and cyclohexyl (2), and Et3PAuS2CNRꞌ2, Rꞌ = Rꞌ = Et (3) and Rꞌ2 = (CH2)4 (4), have been evaluated for antibacterial activity against a panel of 24 Gram positive (8) and Gram negative (16) bacteria. Based on minimum inhibitory concentration (MIC) scores, compounds 1 and 2 were shown to be specifically potent against Gram positive bacteria whereas compounds 3 and, to a lesser extent, 4 exhibited broad range activity. All four compounds were active against methicillin resistant Staphylococcus aureus (MRSA). Time kill assays revealed the compounds to exhibit both time- and concentration-dependent pharmacokinetics against susceptible bacteria. Each compound was bactericidal against one or more bacteria with 3 being especially potent after 8 h exposure; compounds 1 and 3 were bactericidal against MRSA. Compound 3 was the most effective bactericide across the series especially toward B. subtilis, S. saprophyticus, A. hydrophila, P. vulgaris, and V. parahaemolyticus. This study demonstrates the potential of this class of compounds as antibacterial agents, either broad range or against specific bacteria

Three ammonium salts of sulfathiazole: crystallography and anti-microbial assay

The crystal and molecular structures of three ammonium salts derived from sulfathiazole are described. In each case, the anion is in the azanide form, features an intramolecular S←O interaction, and adopts a U-shape. The structures of two cations, [R(HOCH2CH2)NH2]+, namely for R = Me (1) and iPr (2), are unprecedented in the crystallographic literature. Extensive hydrogen bonding is observed in all crystal structures and leads to a two-dimensional array for 1, and three-dimensional architectures for each of 2 and 3 (R = CH2CH2OH). The salts exhibited anti-microbial activity against a range of Gram-positive and Gram-negative bacteria, and proved bactericidal toward Vibrio parahaemolyticus, but had no advantage over sulfathiazole itself

Erratum to: 36th International Symposium on Intensive Care and Emergency Medicine

[This corrects the article DOI: 10.1186/s13054-016-1208-6.]