Second-Order Optimality Conditions for Infinite-Dimensional Quadratic Programs

Journal of Optimization Theory and Applications - Second-order necessary and sufficient optimality conditions for local solutions and locally unique solutions of generalized quadratic programming...     

A new projection method for a class of variational inequalities

In this paper, we revisit the numerical approach to variational inequality problems involving strongly monotone and Lipschitz continuous operators by a variant of projected reflected gradient method. Contrary to what done so far, the resulting algorithm uses a new simple stepsize sequence which is diminishing and nonsummable. This brings the main advantages of the algorithm where the construction of aproximation solutions and the formulation of convergence are done without the prior knowledge of the Lipschitz and strongly monotone constants of cost operators. The assumptions in the formulation of theorem of convergence are also discussed in this paper. Numerical results are reported to illustrate the behavior of the new algorithm and also to compare with others.     

Parallel Algorithms for Solving a Class of Variational Inequalities over the Common Fixed Points Set of a Finite Family of Demicontractive Mappings

Abstract

We propose parallel algorithms for solving a class of variational inequalities over the set of common fixed points for a finite family of demicontractive mappings in real Hilbert spaces. Under some suitable conditions, we prove that the sequence generated by the proposed algorithms converges strongly to a solution of the problem. We apply the proposed algorithms to strongly monotone variational inequality problems with pseudomonotone equilibrium constraints by defining a quasi-nonexpansive and demi-closed mapping whose fixed point set coincides with the solution set of the equilibrium problem.     

Top leads for swine influenza A/H1N1 virus revealed by steered molecular dynamics approach

Since March 2009, the rapid spread of infection during the recent A/H1N1 swine flu pandemic has raised concerns of a far more dangerous outcome should this virus become resistant to current drug therapies. Currently oseltamivir (tamiflu) is intensively used for the treatment of influenza and is reported effective for 2009 A/H1N1 virus. However, as this virus is evolving fast, some drug-resistant strains are emerging. Therefore, it is critical to seek alternative treatments and identify roots of the drug resistance. In this paper, we use the steered molecular dynamics (SMD) approach to estimate the binding affinity of ligands to the glycoprotein neuraminidase. Our idea is based on the hypothesis that the larger is the force needed to unbind a ligand from a receptor the higher its binding affinity. Using all-atom models with Gromos force field 43a1 and explicit water, we have studied the binding ability of 32 ligands to glycoprotein neuraminidase from swine flu virus A/H1N1. The electrostatic interaction is shown to play a more important role in binding affinity than the van der Waals one. We have found that four ligands 141562, 5069, 46080, and 117079 from the NSC set are the most promising candidates to cope with this virus, while peramivir, oseltamivir, and zanamivir are ranked 8, 11, and 20. The observation that these four ligands are better than existing commercial drugs has been also confirmed by our results on the binding free energies obtained by the molecular mechanics-Poisson-Boltzmann surface area (MM-PBSA) method. Our prediction may be useful for the therapeutic application.     

New extragradient methods for solving variational inequality problems and fixed point problems

In this paper, we introduce two new iterative algorithms for finding a common element of the set of fixed points of a quasi-nonexpansive mapping and the set of solutions of the variational inequality problem with a monotone and Lipschitz continuous mapping in real Hilbert spaces, by combining a modified Tseng’s extragradient scheme with the Mann approximation method. We prove weak and strong convergence theorems for the sequences generated by these iterative algorithms. The main advantages of our algorithms are that the construction of solution approximations and the proof of convergence of the algorithms are performed without the prior knowledge of the Lipschitz constant of cost operators. Finally, we provide numerical experiments to show the efficiency and advantage of the proposed algorithms.     

An extension of Krasnoselskii’s fixed point theorem and its application to nonlocal problems for implicit fractional differential systems with uncertainty

The traditional Krasnoselskii’s fixed point theorem in Banach spaces does not reproduce the rich and varied forms of operator equations in abstract spaces which are not linear structure. Consequently, its applications to integral equations and differential equations have met many obstacles. The present alternative Krasnoselskii’s fixed point theorem in generalized semilinear Banach spaces overcomes this deficiency and opens up for profitable investigation such as differential systems with uncertainty. An application to the existence of solutions of nonlocal problems for fuzzy implicit fractional differential systems under Caputo generalized Hukuhara differentiability with demonstrated example is given to validate the effectiveness of our theoretical results.     

The isomeric ratios in photonuclear reactions of natural strontium induced by bremsstrahlungs in the giant dipole resonance region and by 65 MeV bremsstrahlung

We have determined the isomeric ratio of ^85m,gSr in photonuclear reactions of natural strontium induced by bremsstrahlungs with end-point energies in the giant dipole resonance (GDR) region as well as the isomeric ratios of ^85m,gSr and ^84m,gRb produced at 65 MeV bremsstrahlung. In GDR region the target was irradiated at electron accelerator Microtron MT-25 of the Flerov Laboratory of Nuclear Reaction, Joint Institute for Nuclear Research, Dubna, Russia. The target irradiation with 65 MeV bremsstrahlung was performed at the linear electron accelerator of the Pohang Neutron Facility, Pohang, South Korea. The gamma spectra of the samples irradiated in both cases were measured with spectroscopic systems consisting of 8192 channel analyzer and high-energy resolution (180 keV at gamma ray 1332 keV of ⁶⁰Co) HP(Ge) semiconductor detector Canberra. The GENIE2000 (Canberra) computer program was used for data processing. The results were discussed and compared with those of other authors.     

A wavelet particle approximation for McKean–Vlasov and 2D-Navier–Stokes statistical solutions

Letting the initial condition of a PDE be random is interesting when considering complex phenomena. For 2D-Navier–Stokes equations, it is for instance an attempt to take into account the turbulence arising with high velocities and low viscosities. The solutions of these PDEs are random and their laws are called statistical solutions.