MAJOR－EFFICIENT SOLUTIONS AND WEAKLY MAJOR－EFFICIENT SOLUTIONS OF MULTIOBJECTIVE PROGRAMMING

In this papert the theory of major efficiency for multiobjective programmingis established.The major-efficient solutions and weakly major-efficient solutions of multiobjective programming given here are Pareto efficient solutions of the same multiobjectiveprogramming problem, but the converse is not true. In a ceratin sense , these solutionsare in fact better than any other Pareto efficient solutions. Some basic theorems whichcharacterize major-efficient solutions and weakly major-efficient solutions of multiobjective programming are stated and proved. Furthermore,the existence and some geometricproperties of these solutions are studied.

CHARACTERIZATION OF EFFICIENT SOLUTIONS FOR MULTI-OBJECTIVE OPTIMIZATION PROBLEMS INVOLVING SEMI-STRONG AND GENERALIZED SEMI-STRONG E-CONVEXITY

The authors of this article are interested in characterization of efficient solutions for special classes of problems. These classes consider semi-strong E-convexity of involved functions. Sufficient and necessary conditions for a feasible solution to be an efficient or properly efficient solution are obtained.

ε-strongly Efficient Solutions for Vector Optimization with Set-valued Maps

In locally convex Hausdorff topological vector spaces,ε-strongly efficient solutions for vector optimization with set-valued maps are discussed.Firstly,ε-strongly efficient point of set is introduced.Secondly,under the nearly cone-subconvexlike set-valued maps,the theorem of scalarization for vector optimization is obtained.Finally,optimality conditions of ε-strongly efficient solutions for vector optimization with generalized inequality constraints and equality constraints are obtained.

EXISTENCE RESULTS FOR GLOBALLY EFFICIENT SOLUTIONS OF VECTOR EQUILIBRIUM PROBLEMS VIA A GENERALIZED KKM PRINCIPLE

The aim of this article is to present new existence results for globally efficient solutions of a strong vector equilibrium problem given by a sum of two functions via a generalized KKM principle, and to establish the connectedness of the solutions set.

Generating Efficient Solutions in Bilevel Multi-Objective Programming Problems

In this paper, we address bilevel multi-objective programming problems (BMPP) in which the decision maker at each level has multiple objective functions conflicting with each other. Given a BMPP, we show how to construct two artificial multiobjective programming problems such that any point that is efficient for both the two problems is an efficient solution of the BMPP. Some necessary and sufficient conditions for which the obtained result is applicable are provided. A complete procedure of the implementation of an algorithm for generating efficient solutions for the linear case of BMPP is presented. A numerical example is provided to illustrate how the algorithm operates.

Efficient Solution to Electromagnetic Scattering Problems of Bodies of Revolution by Compressive Sensing

Under the theory structure of compressive sensing （CS）, an underdetermined equation is deduced for describing the discrete solution of the electromagnetic integral equation of body of revolution （BOR）, which will result in a small-scale impedance matrix. In the new linear equation system, the small-scale impedance matrix can be regarded as the measurement matrix in CS, while the excited vector is the measurement of unknown currents. Instead of solving dense full rank matrix equations by the iterative method, with suitable sparse representation, for unknown currents on the surface of BOR, the entire current can be accurately obtained by reconstructed algorithms in CS for small-scale undetermined equations. Numerical results show that the proposed method can greatly improve the computgtional efficiency and can decrease memory consumed.

Reasons and Solutions of the Time-consuming College English Teaching with Low Efficiency

College English teaching has been regarded as time- consuming with low efficiency for a long time. This thesis proceeds with the entity of English education in China, deals with the main problems lying in the current college English teaching from 3 perspectives, including the nation and society, teachers, and students, and provides 5 suggestions accordingly.

An Efficient Accurate Direct Solution of Poisson's Equation for Computation of Meteorological Parameters

Poisson's equation is solved numerically by two direct methods, viz. Block Cyclic Reduction (BCR) method and Fourier Method. Qualitative and quantitative comparison between the numerical solutions obtained by two methods indicates that BCR method is superior to Fourier method in terms of speed and accuracy. Therefore. BCR method is applied to solve (?)2(?)= ζ and (?)2X= D from observed vorticity and divergent values. Thereafter the rotational and divergent components of the horizontal monsoon wind in the lower troposphere are reconstructed and are com pared with the results obtained by Successive Over-Relaxation (SOR) method as this indirect method is generally in more use for obtaining the streamfunction ((?)) and velocity potential (X) fields in NWP models. It is found that the results of BCR method are more reliable than SOR method.

Crystallization behaviors of bayerite from sodium chromate alkali solutions

In order to clean production of chromium compounds, it is a critical process to remove aluminates and utilize aluminum compounds from artificial chromate alkali solutions. The effects of Na2 Cr O4 on the neutralization curve, Al（OH）3 precipitation efficiency and induction period of bayerite were investigated. The results indicate that the neutralization curve of the artificial chromate alkali solutions shows three distinct regions and its induction period is longer than that of pure sodium aluminate solutions at the same aluminum concentration. And the decreased temperature and volume fraction of CO2 enhance the particle size of bayerite β-Al（OH）3. Bayerite composed of agglomerates of rods and cone frustums was obtained from alkali metal chromate solutions with 28.5% CO2（volume fraction） at temperatures ranging from 50 °C to 70 °C. Coarse bayerite with particle size（d50） from 24.2 μm to 29.3 μm extremely has few impurities, which is suitable for comprehensive utilization.

Effect of polymer solution structure on displacement efficiency

In this paper, a series of experiments, including atomic force microscope （AFM）, environmental scanning electron microscope （ESEM）, and core displacement tests were conducted to investigate the effect of polymer solution structure on solution properties and oil displacement efficiency. The results show that in the HPAM solution polymer coils were formed and then aggregated into a loose structure, while the HAP2010 solution formed a strong network structure, which would significantly improve the solution viscosity and flow resistance so as to upgrade the capacity of piston-like oil displacement in highly permeable porous media. Meanwhile, the retention of the HAP2010 solution at pore throats were also enhanced, which could reduce water production during subsequent water flooding and enlarge the swept volume during polymer flooding. Therefore, enhancing the interaction among polymer molecules is an effective way to improve the displacement efficiency of polymer solutions in heavy oil reservoirs with high permeability.

Efficient Authentication Scheme for UAV-Assisted Mobile Edge Computing

Preserving privacy is imperative in the new unmanned aerial vehicle(UAV)-assisted mobile edge computing(MEC)architecture to ensure that sensitive information is protected and kept secure throughout the communication.Simultaneously,efficiency must be considered while developing such a privacy-preserving scheme because the devices involved in these architectures are resource constrained.This study proposes a lightweight and efficient authentication scheme for theUAV-assistedMECenvironment.The proposed scheme is a hardware-based password-less authentication mechanism that is based on the fact that temporal and memory-related efficiency can be significantly improved while maintaining the data security by adopting a hardwarebased solution with a simple implementation.The proposed scheme works in four stages:system initialization,EU registration,EU authentication,and session establishment.It is implemented as a single hardware chip comprising registers and XOR gates,and it can run the entire process in one clock cycle.Consequently,the proposed scheme has significantly higher efficiency in terms of runtime and memory consumption compared to other prevalent methods in the area.Simulations are conducted to evaluate the proposed authentication algorithm.The results show that the scheme has an average execution time of 0.986 ms and consumes average memory of 34 KB.The hardware execution time is approximately 0.39 ns,which is a significantly less than the prevalent schemes,whose execution times range in milliseconds.Furthermore,the security of the proposed scheme is examined,and it is resistant to brute-force attacks.Around 1.158×10^(77) trials are required to overcome the system’s security,which is not feasible using fastest available processors.

Power transfer efficiency in an air-breathing radio frequency ion thruster

Due to a series of challenges such as low-orbit maintenance of satellites, the air-breathing electric propulsion has got widespread attention. Commonly, the radio frequency ion thruster is favored by low-orbit missions due to its high specific impulse and efficiency. In this paper, the power transfer efficiency of the radio frequency ion thruster with different gas compositions is studied experimentally, which is obtained by measuring the radio frequency power and current of the antenna coil with and without discharge operation. The results show that increasing the turns of antenna coils can effectively improve the radio frequency power transfer efficiency, which is due to the improvement of Q factor. In pure N_2 discharge,with the increase of radio frequency power, the radio frequency power transfer efficiency first rises rapidly and then exhibits a less steep increasing trend. The radio frequency power transfer efficiency increases with the increase of gas pressure at relatively high power, while declines rapidly at relatively low power. In N_(2)/O_(2) discharge, increasing the N_(2) content at high power can improve the radio frequency power transfer efficiency, but the opposite was observed at low power. In order to give a better understanding of these trends, an analytic solution in limit cases is utilized, and a Langmuir probe was employed to measure the electron density. It is found that the evolution of radio frequency power transfer efficiency can be well explained by the variation of plasma resistance, which is related to the electron density and the effective electron collision frequency.

集值向量拟均衡问题的ε-Henig对偶

首先引入了具集值映射的ε-Henig向量拟均衡问题及其对偶问题,然后在广义凸性与广义Slater条件下讨论了ε-Henig向量拟均衡问题的ε-Henig有效解与其对偶问题的ε-Henig有效解之间的关系,得到了ε-Henig向量拟均衡问题的对偶定理。

集值优化问题E-Henig有效解的稳定性

改善集下的Henig有效解统一了Henig有效解和近似Henig有效解,其稳定性分析在数值计算中不可或缺,同时集值优化问题是当前优化领域研究的热点问题,研究基于改善集下的集值优化问题E-Henig有效解的稳定性具有重要的理论意义和实用价值。首先,针对集值优化问题,基于改善集的概念,引入集值优化问题的E-Henig有效解,统一了集值优化问题近似Henig有效解和Henig有效解;其次,在集值优化问题目标映射和约束条件均扰动的情况下,借助Painlevé-Kuratowski收敛性,建立集值映射水平集的闭凸性、有界性及回收锥的相关性质;然后,借助所获得的集值映射水平集的闭凸性、有界性及回收锥的性质,在集值优化问题目标映射和约束条件均扰动的情况下,分别建立严格真拟C-凸集值优化问题E-弱有效点集、E-Henig有效点集和E-Henig有效解的稳定性结果。所得结果首次聚焦于集值优化问题基于改善集概念下的弱有效点集、Henig有效点集及Henig有效解集的稳定性结果,相较于以往文献大都只关注集值优化问题Henig有效解的存在性、最优性条件、对偶性性质,大大完善了集值优化问题Henig有效解的理论结果,并为数值计算的稳定性分析提供了方法和技巧。

Pareto Efficient Solution and the Class of α-Major Efficient Solutions

As we know, the Pareto efficient (optimal) solution or in other words, thenoninferior solution, is a basic concept in multiobjective programming. In thesense of this kind of solution, much theoretical and application work has been doneon solutions in multiobjective programming since the 1950s. However, because thePareto efficient solution is only a solution with respect to a vector objective beingnoinnferior, as for a given multiobjective programming problem, its set is large whenthe number of objectives is great. This is an inevitable flaw caused by definingPareto efficient solution with the partial order induced by a positive cone. Yu intro-duced the nondominated solution on the basis of a general convex cone or

Benson proper efficiency for vector optimization of generalized subconvexlike set-valued maps in ordered linear spaces

Several equivalent statements of generalized subconvexlike set-valued map are established in ordered linear spaces. Using vector closure, we introduce Benson proper efficient solution of vector optimization problem. Under the assumption of generalized subconvexlikeness, scalarization, multiplier and saddle point theorems are obtained in the sense of Benson proper efficiency.

The Class of the Generalized αk-Major Efficient Solutions for Multi-objective Programming

This paper proposes the concepts of generalized αk-major efficient solutions and generalized αk- major optimal solutions for multi-objective programming, and studies their some important properties.

THE COMPARISON-NUMBER METHOD FOR FINDING MAJOR OPTIMAL SOLUTIONS AND MAJOR EFFICIENT SOLUTIONS OF THE DISCRETE MULTIOBJECTIVE PROGRAMMING

In this paper, we introduce the comparison number for one feasible solutioncompared with another. With the help of it the comparison-number method for find-ing the major optimal solutions aud major efficient solutions to discrete multiobjectiveprogramming is given.

CHARACTERIZATIONS OF PROPER EFFICIENT SOLUTIONS IN TERMS OF SADDLE POINTS AND DUALITY

In this paper we characterize the proper efficient solution of a mul-tiobjective programming problem(P)in terms of the saddle point criterion of anew problem(S)and establish a pair of dual problems(S_α)and(D_α)in order todecide the proper efficient solution by the strong duality.We also give methodof characterization in terms of the saddle point criterion of(P).Finally,we provethat every efficient solution of the matrix linear programming problem is a properefficient solution.

NECESSARY CONDITIONS FOR MAJOR OPTIMAL SOLUTIONS AND MAJOR EFFICIENT SOLUTIONS OF MULTIOBJECTIVE PROGRAMMING

In this papers the Fritz John conditions and Kuhn-Tucker conditions for majoroptimal solutions and major efficient solutions of multiobjective programming are givenand proved.