A general algorithm for multiple-sets split feasibility problem involving resolvents and Bregman mappings

In this paper, by using Bregman distance, we introduce a new iterative process involving products of resolvents of maximal monotone operators for approximating a common element of the set of common fixed points of a finite family of multi-valued Bregman relatively nonexpansive mappings and the solution set of the multiple-sets split feasibility problem and common zeros of maximal monotone operators. We derive a strong convergence theorem of the proposed iterative algorithm under appropriate situations. Finally, we mention several corollaries and two applications of our algorithm.     

Viscosity Approximation Methods for Generalized Multi-Valued Nonexpansive Mappings with Applications

Abstract

In this article, we study viscosity approximation methods for generalized multi-valued nonexpansive mappings and we present some new results related to strong convergence, variational inequality, convex optimization, split and common split feasibility problems (SFPs). Some numerical computations are also presented to illustrate our results.     

关于有限族Lipschitz映射多步Ishikawa迭代算法的收敛性及其应用

本文的目的是研究Lipschitz映射公共不动点问题.基于传统的Ishikawa迭代和Noor迭代方法,我们引入多步Ishikawa迭代算法,并且分别给出了该算法强收敛于有限族拟-Lipschitz映射和伪压缩映射公共不动点的充分必要条件.此外,我们证明了该算法强收敛到非扩张映射的公共不动点.作为应用,我们给出数值试验证实所得的结论.     

Asymptotic behavior of averaged and firmly nonexpansive mappings in geodesic spaces

We further study averaged and firmly nonexpansive mappings in the setting of geodesic spaces with a main focus on the asymptotic behavior of their Picard iterates. We use methods of proof mining to obtain an explicit quantitative version of a generalization to geodesic spaces of a result on the asymptotic behavior of Picard iterates for firmly nonexpansive mappings proved by Reich and Shafrir. From this result we obtain effective uniform bounds on the asymptotic regularity for firmly nonexpansive mappings. Besides this, we derive effective rates of asymptotic regularity for sequences generated by two algorithms used in the study of the convex feasibility problem in a nonlinear setting.     

Non-isothermal kinetic analysis and feasibilty study of medium grade crude oil field

In this research, non-isothermal kinetics and feasibility study of medium grade crude oil is studied in the presence of a limestone matrix. Experiments were performed at a heating rate of 10°C min⁻¹, whereas the air flow rate was kept constant at 50 mL min⁻¹ in the temperature range of 20 to 600°C (DSC) and 20 to 900°C (TG). In combustion with air, three distinct reaction regions were identified in all crude oil/limestone mixtures, known as low temperature oxidation (LTO), fuel deposition (FD) and high temperature oxidation (HTO). The activation energy values were in the order of 5–9 kJ mol⁻¹ in LTO region and 189–229 kJ mol⁻¹ in HTO region. It was concluded that the medium grade crude oil field was not feasible for a self-sustained combustion process.     

On the finite termination of the Douglas-Rachford method for the convex feasibility problem

In this paper we apply the Douglas–Rachford (DR) method to solve the problem of finding a point in the intersection of the interior of a closed convex cone and a closed convex set in an infinite-dimensional Hilbert space. For this purpose, we propose two variants of the DR method which can find a point in the intersection in a finite number of iterations. In order to analyse the finite termination of the methods, we use some properties of the metric projection and a result regarding the rate of convergence of fixed point iterations. As applications of the results, we propose the methods for solving the conic and semidefinite feasibility problems, which terminate at a solution in a finite number of iterations.     

Some subgradient extragradient type algorithms for solving split feasibility and fixed point problems

In this paper, we consider the split feasibility problem (SFP) in infinite‐dimensional Hilbert spaces and propose some subgradient extragradient‐type algorithms for finding a common element of the fixed‐point set of a strict pseudocontraction mapping and the solution set of a split feasibility problem by adopting Armijo‐like stepsize rule. We derive convergence results under mild assumptions. Our results improve some known results from the literature. Copyright © 2016 John Wiley & Sons, Ltd.     

A NEW PERTURBATION SIMPLEX ALGORITHM FOR LINEAR PROGRAMMING

1.IntroductionThedualsimplexalgorithm[1,91andtheprimal-dualsimplealgorithm[6]arewellknownandefficientsimplexvariants.However,bothofthemneedaninitialdualfeasiblebasistogetstarted,andthereforecannotbedirectlyappliedtosolvingproblemsthatdonothavesuchane...     

Enrichment of Zinc and Iron Micronutrients in Lentil (Lens culinaris Medik.) through Biofortification

Biofortification of pulse crops with Zn and Fe is a viable approach to combat their widespread deficiencies in humans. Lentil (Lens culinaris Medik.) is a widely consumed edible crop possessing a high level of Zn and Fe micronutrients. Thus, the present study was conducted to examine the influence of foliar application of Zn and Fe on productivity, concentration, uptake and the economics of lentil cultivation (LL 931). For this, different treatment combinations of ZnSO₄·7H₂O (0.5%) and FeSO₄·7H₂O (0.5%), along with the recommended dose of fertilizer (RDF), were applied to the lentil. The results of study reported that the combined foliar application of ZnSO₄·7H₂O (0.5%) + FeSO₄·7H₂O (0.5%) at pre-flowering (S1) and pod formation (S2) stages was most effective in enhancing grain and straw yield, Zn and Fe concentration, and uptake. However, the outcome of this treatment was statistically on par with the results obtained under the treatment ZnSO₄·7H₂O (0.5%) + FeSO₄·7H₂O (0.5%) at S1 stage. A single spray of ZnSO₄·7H₂O (0.5%) + FeSO₄·7H₂O (0.5%) at S1 stage enhanced the grain and straw yield up to 39.6% and 51.8%, respectively. Similarly, Zn and Fe concentrations showed enhancement in grain (10.9% and 20.4%, respectively) and straw (27.5% and 27.6% respectively) of the lentil. The increase in Zn and Fe uptake by grain was 54.8% and 68.0%, respectively, whereas uptake by straw was 93.6% and 93.7%, respectively. Also the benefit:cost was the highest (1.96) with application of ZnSO₄·7H₂O (0.5%) + FeSO₄·7H₂O (0.5%) at S1 stage. Conclusively, the combined use of ZnSO₄·7H₂O (0.5%) + FeSO₄·7H₂O (0.5%) at S1 stage can contribute significantly towards yield, Zn and Fe concentration, as well as uptake and the economic returns of lentil to remediate the Zn and Fe deficiency.