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.

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.

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.

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.

A FLEXIBLE OBJECTIVE-CONSTRAINT APPROACH AND A NEW ALGORITHM FOR CONSTRUCTING THE PARETO FRONT OF MULTIOBJECTIVE OPTIMIZATION PROBLEMS

In this article, a novel scalarization technique, called the improved objective-constraint approach, is introduced to find efficient solutions of a given multiobjective programming problem. The presented scalarized problem extends the objective-constraint problem. It is demonstrated that how adding variables to the scalarized problem, can lead to find conditions for (weakly, properly) Pareto optimal solutions. Applying the obtained necessary and sufficient conditions, two algorithms for generating the Pareto front approximation of bi-objective and three-objective programming problems are designed. These algorithms are easy to implement and can achieve an even approximation of (weakly, properly) Pareto optimal solutions. These algorithms can be generalized for optimization problems with more than three criterion functions, too. The effectiveness and capability of the algorithms are demonstrated in test problems.

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.

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.

EKELAND'S PRINCIPLE FOR SET-VALUED VECTOR EQUILIBRIUM PROBLEMS

In this paper, we introduce a concept of quasi C-lower semicontinuity for setvalued mapping and provide a vector version of Ekeland＇s theorem related to set-valued vector equilibrium problems. As applications, we derive an existence theorem of weakly efficient solution for set-valued vector equilibrium problems without the assumption of convexity of the constraint set and the assumptions of convexity and monotonicity of the set-valued mapping. We also obtain an existence theorem of ε-approximate solution for set-valued vector equilibrium problems without the assumptions of compactness and convexity of the constraint set.

Sufficient Optimality Conditions for Multiobjective Programming Involving (V, ρ)h,ψ-type Ⅰ Functions

New classes of functions namely (V, ρ)_(h,φ)-type I, quasi (V, ρ)_(h,φ)-type I and pseudo (V, ρ)_(h,φ)-type I functions are defined for multiobjective programming problem by using BenTal's generalized algebraic operation. The examples of (V, ρ)_(h,φ)-type I functions are given. The sufficient optimality conditions are obtained for multi-objective programming problem involving above new generalized convexity.

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 Duality on Vector Optimization Problems

Duality framework on vector optimization problems in a locally convex topological vector space are established by using scalarization with a cone-strongly increasing function.The dualities for the scalar convex composed optimization problems and for general vector optimization problems are studied.A general approach for studying duality in vector optimization problems is presented.

Optimal indicator for changing the filter during the continuous renal replacement therapy in intensive care unit patients with acute kidney injury:A crossover randomized trial

BACKGROUND:The study aims to investigate an optimal indicator for changing the filter during the continuous renal replacement therapy(CRRT)in intensive care unit(ICU)patients with acute kidney injury(AKI).METHODS:Patients with AKI requiring CRRT in an ICU were randomly divided into two groups for crossover trial,i.e.,groups A and B.Patients in the group A were firstly treated with continuous veno-venous hemofiltration(CVVH),followed by continuous veno-venous hemodiafiltration(CVVHDF).Patients in the group B were firstly treated with CVVHDF followed by CVVH.Delivered doses of solutes with different molecular weights at the indicated time points between groups were compared.A correlation analysis between the delivered dose and pre-filter pressure(P_(PRE))and transmembrane pressure(P_(TM))was performed.Receiver operating characteristic(ROC)curves were constructed to evaluate the accuracy of P_(TM) as an indicator for filter replacement.RESULTS:A total of 50 cases were analyzed,27 in the group A and 23 in the group B.Delivered doses of different molecular-weight solutes significantly decreased before changing the filter in both modalities,compared with those at the initiation of treatment(all P<0.05).In the late stage of CRRT,the possible rebound of serum medium-molecular-weight solute concentration was observed.P_(TM) was negatively correlated with the delivered dose of medium-molecular-weight solute in both modalities.The threshold for predicting the rebound of serum concentration of medium-molecularweight solute by P_(TM) was 146.5 mm Hg(1 mm Hg=0.133 k Pa).CONCLUSIONS:The filter can be used as long as possible within the manufacturer’s safe use time limits to remove small-molecular-weight solutes.P_(TM) of 146.5 mm Hg may be an optimal indicator for changing the filter in CRRT therapies to remove medium-molecular-weight solutes.

METHOD OF CENTERS ALGORITHM FORMULTI-OBJECTIVE PROGRAMMING PROBLEMS

In this paper, we consider a method of centers for solving multi-objective programming problems, where the objective functions involved are concave functions and the set of feasible points is convex. The algorithm is defined so that the sub-problems that must be solved during its execution may be solved by finite-step procedures. Conditions are given under which the algorithm generates sequences of feasible points and constraint multiplier vectors that have accumulation points satisfying the KKT conditions. Finally, we establish convergence of the proposed method of centers algorithm for solving multiobjective programming problems.

The Optimality Conditions for Multiobjective Semi-infinite Programming Involving Generalized Unified （C, α, p, d）-convexity

The definition of generalized unified (C, α, ρ, d)-convex function is given. The concepts of generalized unified (C, α, ρ, d)-quasiconvexity, generalized unified (C, α, ρ, d)-pseudoconvexity and generalized unified (C, α, ρ, d)-strictly pseudoconvex functions are presented. The sufficient optimality conditions for multiobjective nonsmooth semi-infinite programming are obtained involving these generalized convexity lastly.

Nondifferentiable Multiobjective Programming under Generalized d_I-G-Type I Invexity

To relax convexity assumptions imposed on the functions in theorems on sufficient conditions and duality,new concepts of generalized d I-G-type I invexity were introduced for nondifferentiable multiobjective programming problems.Based upon these generalized invexity,G-Fritz-John(G-F-J)and G-KarushKuhn-Tucker(G-K-K-T)types sufficient optimality conditions were established for a feasible solution to be an efficient solution.Moreover,weak and strict duality results were derived for a GMond-Weir type dual under various types of generalized d I-G-type I invexity assumptions.

Fourier time spectral method for subsonic and transonic flows

The time accuracy of the exponentially accurate Fourier time spectral method（TSM） is examined and compared with a conventional 2nd-order backward difference formula（BDF） method for periodic unsteady flows. In particular, detailed error analysis based on numerical computations is performed on the accuracy of resolving the local pressure coefficient and global integrated force coefficients for smooth subsonic and non-smooth transonic flows with moving shock waves on a pitching airfoil. For smooth subsonic flows, the Fourier TSM method offers a significant accuracy advantage over the BDF method for the prediction of both the local pressure coefficient and integrated force coefficients. For transonic flows where the motion of the discontinuous shock wave contributes significant higherorder harmonic contents to the local pressure fluctuations,a sufficient number of modes must be included before the Fourier TSM provides an advantage over the BDF method.The Fourier TSM, however, still offers better accuracy than the BDF method for integrated force coefficients even for transonic flows. A problem of non-symmetric solutions for symmetric periodic flows due to the use of odd numbers of intervals is uncovered and analyzed. A frequency-searching method is proposed for problems where the frequency is not known a priori. The method is tested on the vortex shedding problem of the flow over a circular cylinder.

Multiobjective Stochastic Linear Programming: An Overview

Many Optimization problems in engineering and economic involve the challenging task of pondering both conflicting goals and random data. In this paper, we give an up-to-date overview of how important ideas from optimization, probability theory and multicriteria decision analysis are interwoven to address situations where the presence of several objective functions and the stochastic nature of data are under one roof in a linear optimization context. In this way users of these models are not bound to caricature their problems by arbitrarily squeezing different objective functions into one and by blindly accepting fixed values in lieu of imprecise ones.

Necessary Optimality Conditions for Multi-Objective Semi-Infinite Variational Problem

In this paper, necessary optimality conditions for a class of Semi-infinite Variational Problems are established which are further generalized to a class of Multi-objective Semi-Infinite Variational Problems. These conditions are responsible for the development of duality theory which is an extremely important feature for any class of problems, but the literature available so far lacks these necessary optimality conditions for the stated problem. A lemma is also proved to find the topological dual of as it is required to prove the desired result.

ON MULTIOBJECTIVE FRACTIONAL PROGRAMS

In this paper some optimality criteria are proved and some Mond\|Weir type duality theorem for multiobjective fractional programming problems defined in a Banach space is obtained.

Mixing of two different electrolyte solutions in electromagnetic rectangular mixers

This study proposes a new electromagnetic rectangular mixer, and numerically examines the mixing characteristics of two different electrolyte solutions in the device under a uniform magnetic field. The mixer consists of a conduit with electrodes equipped on its top and bottom walls. The difference in the electric potentials applied to the sets of electrodes induces the current. The combination of the induced current and magnetic field yields Lorentz force, resulting in the fluid motion for pumping and mixing of the two different fluids. The numerical simulation is carried out with the use of commercial software CFX. The present numerical model is validated by an existing numerical work. The effect of different variables on mixing efficiency is investigated in many different cases with two different heights of the duct and various input voltages of the electrodes. The current simulation results indicate that the mixing performance can be enhanced by using multiple sets of electrodes and applying higher input voltages（absolute values） to the electrodes.