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 pr...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.展开更多
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 algebr...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.展开更多
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 compos...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.展开更多
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:Pati...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.展开更多
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 unif...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.展开更多
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 programmi...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.展开更多
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 optimi...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.展开更多
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 co...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.展开更多
Radio frequency identification (RFID) is one of today s most anticipated technologies for a broad range of enterprises. Based on the promise of lower operating costs combined with more accurate product and asset infor...Radio frequency identification (RFID) is one of today s most anticipated technologies for a broad range of enterprises. Based on the promise of lower operating costs combined with more accurate product and asset information, organizations .Rfrom manufacturers to government agencies, retailers to healthcare providers , Rare introducing RFID technologies in the supply chain, for asset tracking and management, and for security and regulatory purposes.展开更多
This paper aims at studying optimality conditions of robust weak efficient solutions for a nonsmooth uncertain multi-objective fractional programming problem(NUMFP).The concepts of two types of generalized convex func...This paper aims at studying optimality conditions of robust weak efficient solutions for a nonsmooth uncertain multi-objective fractional programming problem(NUMFP).The concepts of two types of generalized convex function pairs,called type-I functions and pseudo-quasi-type-I functions,are introduced in this paper for(NUMFP).Under the assumption that(NUMFP)satisfies the robust constraint qualification with respect to Clarke subdifferential,necessary optimality conditions of the robust weak efficient solution are given.Sufficient optimality conditions are obtained under pseudo-quasi-type-I generalized convexity assumption.Furthermore,we introduce the concept of robust weak saddle points to(NUMFP),and prove two theorems about robust weak saddle points.The main results in the present paper are verified by concrete examples.展开更多
The notion of higher-order B-type I functional is introduced in this paper.This notion is utilized to study optimality and duality for multiobjective semi-infinite variational problem in which the index set of inequal...The notion of higher-order B-type I functional is introduced in this paper.This notion is utilized to study optimality and duality for multiobjective semi-infinite variational problem in which the index set of inequality constraints is an infinite set.The concept of efficiency is used as a tool for optimization.Mond–Weir type of dual is proposed for which weak,strong,and strict converse duality theorems are proved to relate efficient solutions of primal and dual problems.展开更多
This paper first applies the fuzzy set theory to multi-objective semi-definite program-ming (MSDP), and proposes the fuzzy multi-objective semi-definite programming (FMSDP) model whose optimal efficient solution is de...This paper first applies the fuzzy set theory to multi-objective semi-definite program-ming (MSDP), and proposes the fuzzy multi-objective semi-definite programming (FMSDP) model whose optimal efficient solution is defined for the first time, too. By constructing a membership function, the FMSDP is translated to the MSDP. Then we prove that the optimal efficient solution of FMSDP is consistent with the efficient solution of MSDP and present the optimality condition about these programming. At last, we give an algorithm for FMSDP by introducing a new membership function and a series of transformation.展开更多
The main goal of this paper is to introduce necessary efficiency conditionsfor a class of multi-time vector fractional variational problems with nonlinear equal-ity and inequality constraints involving higher-order pa...The main goal of this paper is to introduce necessary efficiency conditionsfor a class of multi-time vector fractional variational problems with nonlinear equal-ity and inequality constraints involving higher-order partial derivatives.We considerthe multi-time multiobjective variational problem(MFP)of minimizing a vector ofpath-independent curvilinear integral functionals quotients subject to PDE and/or PDIconstraints,developing an optimization theory on the higher-order jet bundles.展开更多
文摘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.
基金Supported by the NSF of Shaanxi Provincial Educational Department(06JK152)
文摘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.
基金Supported by the Natural Science Foundation of Fujian Province（S0650021）
文摘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.
基金supported by Kunshan Science and Technology Special Fund(Social Development Category,KS18040)。
文摘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.
基金Supported by the Science Foundation of Shaanxi Provincial Educational Department Natural Science Foundation of China（06JK152） Supported by the Graduate Innovation Project of Yanan uni- versity（YCX201003）
文摘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.
基金National Natural Science Foundation of China(No.11071110)
文摘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.
文摘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.
文摘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.
文摘Radio frequency identification (RFID) is one of today s most anticipated technologies for a broad range of enterprises. Based on the promise of lower operating costs combined with more accurate product and asset information, organizations .Rfrom manufacturers to government agencies, retailers to healthcare providers , Rare introducing RFID technologies in the supply chain, for asset tracking and management, and for security and regulatory purposes.
基金supported by Natural Science Foundation of China(Nos.11861002 and 12171601)the Key Project of North Minzu University(No.ZDZX201804)+1 种基金the Construction Project of First-Class Disciplines in Ningxia Higher Education(NXYLXK2017B09)the Postgraduate Innovation Project of North Minzu Universit(No.YCX21157)..
文摘This paper aims at studying optimality conditions of robust weak efficient solutions for a nonsmooth uncertain multi-objective fractional programming problem(NUMFP).The concepts of two types of generalized convex function pairs,called type-I functions and pseudo-quasi-type-I functions,are introduced in this paper for(NUMFP).Under the assumption that(NUMFP)satisfies the robust constraint qualification with respect to Clarke subdifferential,necessary optimality conditions of the robust weak efficient solution are given.Sufficient optimality conditions are obtained under pseudo-quasi-type-I generalized convexity assumption.Furthermore,we introduce the concept of robust weak saddle points to(NUMFP),and prove two theorems about robust weak saddle points.The main results in the present paper are verified by concrete examples.
基金Jyoti was supported by University Grant Commission Non-NET research fellowship,India(No.Schs/Non-NET/139/Ext-142/2015-16/1931).
文摘The notion of higher-order B-type I functional is introduced in this paper.This notion is utilized to study optimality and duality for multiobjective semi-infinite variational problem in which the index set of inequality constraints is an infinite set.The concept of efficiency is used as a tool for optimization.Mond–Weir type of dual is proposed for which weak,strong,and strict converse duality theorems are proved to relate efficient solutions of primal and dual problems.
基金Supported by the National Natural Science Foundation of China (Grant No.10671057)
文摘This paper first applies the fuzzy set theory to multi-objective semi-definite program-ming (MSDP), and proposes the fuzzy multi-objective semi-definite programming (FMSDP) model whose optimal efficient solution is defined for the first time, too. By constructing a membership function, the FMSDP is translated to the MSDP. Then we prove that the optimal efficient solution of FMSDP is consistent with the efficient solution of MSDP and present the optimality condition about these programming. At last, we give an algorithm for FMSDP by introducing a new membership function and a series of transformation.
文摘The main goal of this paper is to introduce necessary efficiency conditionsfor a class of multi-time vector fractional variational problems with nonlinear equal-ity and inequality constraints involving higher-order partial derivatives.We considerthe multi-time multiobjective variational problem(MFP)of minimizing a vector ofpath-independent curvilinear integral functionals quotients subject to PDE and/or PDIconstraints,developing an optimization theory on the higher-order jet bundles.
