Proximal type algorithms involving linesearch and inertial technique for split variational inclusion problem in hilbert spaces with applications

ABSTRACT

In convex optimization, numerous problems in applied sciences can be modelled as the split variational inclusion problem (SVIP). In this connection, we aim to design new and efficient proximal type algorithms which are based on the inertial technique and the linesearches terminology. We then discuss its convergence under some suitable conditions without the assumption on the operator norm. We also apply our main result to the split minimization problem, the split feasibility problem, the relaxed split feasibility problem and the linear inverse problem. Finally, we provide some numerical experiments and comparisons to these problems. The obtained result mainly improves the recent results investigated by Chuang.     

Self-dual Yang-Mills equations in split signature

We study the self-dual Yang-Mills equations in split signature. We give a special solution, called the basic split instanton, and describe the ADHM construction in the split signature. Moreover a split version of t'Hooft ansatz is described.     

Splits of circuits

This paper discusses an attempt at identifying a property of circuits in (nonplanar) graphs resembling the separation property of circuits in planar graphs derived from the Jordan Curve Theorem.If G is a graph and C is a circuit in G, we say that two circuits in G form a split of C if the symmetric difference of their edges sets is equal to the edge set of C, and if they are separated in G by the intersection of their vertex sets.García Moreno and Jensen, A note on semiextensions of stable circuits, Discrete Math. 309 (2009) 4952-4954, asked whether such a split exists for any circuit C whenever G is 3-connected. We observe that if true, this implies a strong form of a version of the Cycle Double-Cover Conjecture suggested in the Ph.D. thesis of Luis Goddyn. The main result of the paper shows that the property holds for Hamilton circuits in cubic graphs.     

The hardness of approximating the boxicity, cubicity and threshold dimension of a graph

A k-dimensional box is the Cartesian product R₁×R₂×?×R_k where each R_i is a closed interval on the real line. The boxicity of a graph G, denoted as , is the minimum integer k such that G can be represented as the intersection graph of a collection of k-dimensional boxes. A unit cube in k-dimensional space or a k-cube is defined as the Cartesian product R₁×R₂×?×R_k where each R_i is a closed interval on the real line of the form [a_i,a_i+1]. The cubicity of G, denoted as , is the minimum integer k such that G can be represented as the intersection graph of a collection of k-cubes. The threshold dimension of a graph G(V,E) is the smallest integer k such that E can be covered by k threshold spanning subgraphs of G. In this paper we will show that there exists no polynomial-time algorithm for approximating the threshold dimension of a graph on n vertices with a factor of O(n^0.5−?) for any ?>0 unless NP=ZPP. From this result we will show that there exists no polynomial-time algorithm for approximating the boxicity and the cubicity of a graph on n vertices with factor O(n^0.5−?) for any ?>0 unless NP=ZPP. In fact all these hardness results hold even for a highly structured class of graphs, namely the split graphs. We will also show that it is NP-complete to determine whether a given split graph has boxicity at most 3.     

A note on branch-and-cut-and-price

In this paper, we propose a methodology for branch-and-cut-and-price when cuts and columns are generated simultaneously. The methodology is illustrated with two application cases: the Split Delivery Vehicle Routing Problem (SDVRP) and the Bus Rapid Transit Route Design Problem (BRTRDP).     

The glass insert in stop-flow split injection

Summary In stop-flow split injection the careful choice of the experimental conditions is of great importance for accurate quantitation, the size of the gaseous sample plug and its position with respect to the column inlet and to the top of the insert during the evaporation period are critical to prohibit sample vapour overflow and aerosol splitting. The proper insert design is established. A sample volume of 0.5 l is recommended in the practical application of the stop-flow method.     

ZrO2∶Er3+,Yb3+纳米晶的制备及Er3+离子能级在晶体场中的分裂

采用1,3-丁二醇低热结晶法制备了ZrO2∶Er3+,Yb3+纳米晶.常温下,用980nm的红外激光激发可以观察到很强的ZrO2∶Er3+,Yb3+纳米晶红光发射,用荧光光谱仪记录了该上转换光谱.X射线粉末衍射(XRD)结果表明,ZrO2∶Er3+,Yb3+纳米晶属于立方晶系.研究了纳米晶的上转换发光机理,根据晶体场理论对Er3+的2个上转换能级进行了Stark分裂计算,对2个能级之间的谱线进行了归属,进一步证实了980nm激发Er3+离子的上转换经历两个过程:一是连续吸收2个980nm光子的过程,二是吸收980nm光子,电子转移到亚稳态能级后,再吸收980nm光子的过程     

Injection temperature effects using On-column and split sampling in capillary gas chromatography

The effect of sample injection temperature on quantitation is examined for on-column and conventional split modes of sampling in capillary gas chromatography. Discrimination effects can be observed even with on-column injection if the injection temperature is too far above the boiling point of the solvent (or that of a major low boiling constituent(. This is attributed to higher boiling components being left behind in the syringe needle, and a set of simulation experiments are described to illustrate this effect. Various discrimination patterns using conventional split injection were observed, depending on temperature of injection. Apart from syringe needle effects, discrimination is probably due to the preferential venting of higher boiling components as liquid sample droplets, which can have a lifetime greater than the time of transit to the splitter. With such a two-phase system, involving variable droplet size, the flow distribution in the splitter will be critical to uniform sampling. The use of combination on-column/split sampling, with the appropriate temperature control to provide sample uniformity to the splitter is discussed as an advantageous alternative to conventional split sampling.     

Graph theoretic approach to parallel gene assembly

We study parallel complexity of signed graphs motivated by the highly complex genetic recombination processes in ciliates. The molecular gene assembly operations have been modeled by operations of signed graphs, i.e., graphs where the vertices have a sign + or −. In the optimization problem for signed graphs one wishes to find the parallel complexity by which the graphs can be reduced to the empty graph. We relate parallel complexity to matchings in graphs for some natural graph classes, especially bipartite graphs. It is shown, for instance, that a bipartite graph G has parallel complexity one if and only if G has a unique perfect matching. We also formulate some open problems of this research topic.     

一类新的车辆路径问题及其两阶段算法

本文结合汽车零部件第三方物流业的实际背景,提出了一类新的车辆路径问题,它是一种带时间窗约束的分车运输同时收发车辆路径问题(简称SVRPSPDTW).接着给出了问题的模型,并提出求解问题的启发式算法：两阶段算法. 最后在改进的Solomn的算例的基础上,进行了数值试验.