Every year, around the world, between 250,000 and 500,000 people suffer a spinal cord injury(SCI). SCI is a devastating medical condition that arises from trauma or disease-induced damage to the spinal cord, disruptin...Every year, around the world, between 250,000 and 500,000 people suffer a spinal cord injury(SCI). SCI is a devastating medical condition that arises from trauma or disease-induced damage to the spinal cord, disrupting the neural connections that allow communication between the brain and the rest of the body, which results in varying degrees of motor and sensory impairment. Disconnection in the spinal tracts is an irreversible condition owing to the poor capacity for spontaneous axonal regeneration in the affected neurons.展开更多
During the use of robotics in applications such as antiterrorism or combat,a motion-constrained pursuer vehicle,such as a Dubins unmanned surface vehicle(USV),must get close enough(within a prescribed zero or positive...During the use of robotics in applications such as antiterrorism or combat,a motion-constrained pursuer vehicle,such as a Dubins unmanned surface vehicle(USV),must get close enough(within a prescribed zero or positive distance)to a moving target as quickly as possible,resulting in the extended minimum-time intercept problem(EMTIP).Existing research has primarily focused on the zero-distance intercept problem,MTIP,establishing the necessary or sufficient conditions for MTIP optimality,and utilizing analytic algorithms,such as root-finding algorithms,to calculate the optimal solutions.However,these approaches depend heavily on the properties of the analytic algorithm,making them inapplicable when problem settings change,such as in the case of a positive effective range or complicated target motions outside uniform rectilinear motion.In this study,an approach employing a high-accuracy and quality-guaranteed mixed-integer piecewise-linear program(QG-PWL)is proposed for the EMTIP.This program can accommodate different effective interception ranges and complicated target motions(variable velocity or complicated trajectories).The high accuracy and quality guarantees of QG-PWL originate from elegant strategies such as piecewise linearization and other developed operation strategies.The approximate error in the intercept path length is proved to be bounded to h^(2)/(4√2),where h is the piecewise length.展开更多
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 efficie...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.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
A new concept of(Φ,ρ,α)-V-invexity for differentiable vector-valued functions is introduced,which is a generalization of differentiable scalar-valued(Φ,ρ)-invexity.Based upon the(Φ,ρ,α)-V-invex functions,suffi...A new concept of(Φ,ρ,α)-V-invexity for differentiable vector-valued functions is introduced,which is a generalization of differentiable scalar-valued(Φ,ρ)-invexity.Based upon the(Φ,ρ,α)-V-invex functions,sufficient optimality conditions and MondWeir type dual theorems are derived for a class of nondifferentiable multiobjective fractional programming problems in which every component of the objective function and each constraint function contain a term involving the support function of a compact convex set.展开更多
This paper deals with the connectedness of the cone-efficient solution set for vector optimization in locally convex Hausdorff topological vector spaces. The connectedness of the cone-efficient solution set is proved ...This paper deals with the connectedness of the cone-efficient solution set for vector optimization in locally convex Hausdorff topological vector spaces. The connectedness of the cone-efficient solution set is proved for multiobjective programming defined by a continuous one-to-one cone-quasiconvex mapping on a compact convex set of alternatives. During the proof, the generalized saddle theorem plays a key role.展开更多
In this paper, optimality conditions for multiobjective programming problems having V-invex objective and constraint functions are considered. An equivalent multiobjective programming problem is constructed by a modif...In this paper, optimality conditions for multiobjective programming problems having V-invex objective and constraint functions are considered. An equivalent multiobjective programming problem is constructed by a modification of the objective function.Furthermore, a (α, η)-Lagrange function is introduced for a constructed multiobjective programming problem, and a new type of saddle point is introduced. Some results for the new type of saddle point are given.展开更多
This paper studies a class of multiobjective generalized fractional programming problems, where the numerators of objective functions are the sum of differentiable function and convex function, while the denominators ...This paper studies a class of multiobjective generalized fractional programming problems, where the numerators of objective functions are the sum of differentiable function and convex function, while the denominators are the difference of differentiable function and convex function. Under the assumption of Calmness Constraint Qualification the Kuhn-Tucker type necessary conditions for efficient solution are given, and the Kuhn-Tucker type sufficient conditions for efficient solution are presented under the assumptions of （F, α, ρ, d）-V-convexity. Subsequently, the optimality conditions for two kinds of duality models are formulated and duality theorems are proved.展开更多
For a multiobjective bilevel programnfing problem （P） with an extremal-value function, its dual problem is constructed by using the Fenchel-Moreau conjugate of the functions involved. Under some convexity and monoto...For a multiobjective bilevel programnfing problem （P） with an extremal-value function, its dual problem is constructed by using the Fenchel-Moreau conjugate of the functions involved. Under some convexity and monotonicity assumptions, the weak and strong duality assertions are obtained.展开更多
In this paper, we obtain some other properties of the majorly efficient points and solutions of the multiobjective optimization presellted in two previous papers of Hu. By decomposing the major cone, which is non-poin...In this paper, we obtain some other properties of the majorly efficient points and solutions of the multiobjective optimization presellted in two previous papers of Hu. By decomposing the major cone, which is non-pointed, non-convex and non-closed into a finite union of disjoint strictly supported pointed convex cones, we discuss the continuous perturbations of the decision space. Several sufficient conditions for the continuity of the sets of majorly efficiellt points and solutions are given.展开更多
Multiple objective stochastic linear programming is a relevant topic. As a matter of fact, many practical problems ranging from portfolio selection to water resource management may be cast into this framework. Severe ...Multiple objective stochastic linear programming is a relevant topic. As a matter of fact, many practical problems ranging from portfolio selection to water resource management may be cast into this framework. Severe limitations on objectivity are encountered in this field because of the simultaneous presence of randomness and conflicting goals. In such a turbulent environment, the mainstay of rational choice cannot hold and it is virtually impossible to provide a truly scientific foundation for an optimal decision. In this paper, we resort to the bounded rationality principle to introduce satisfying solution for multiobjective stochastic linear programming problems. These solutions that are based on the chance-constrained paradigm are characterized under the assumption of normality of involved random variables. Ways for singling out such solutions are also discussed and a numerical example provided for the sake of illustration.展开更多
This study addresses bilevel linear multi-objective problem issues i.e the special case of bilevel linear programming problems where each decision maker has several objective functions conflicting with each other. We ...This study addresses bilevel linear multi-objective problem issues i.e the special case of bilevel linear programming problems where each decision maker has several objective functions conflicting with each other. We introduce an artificial multi-objective linear programming problem of which resolution can permit to generate the whole feasible set of the upper level decisions. Based on this result and depending if the leader can evaluate or not his preferences for his different objective functions, two approaches for obtaining Pareto- optimal solutions are presented.展开更多
In this paper, two duality results are established under generalized ρ-convexity conditions for a class of multiobjective fractional programmign involvign differentiable n-sten functions.
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 dI-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 dI-G-type Ⅰ invexity were introduced for nondifferentiable multiobjective programming problems.Based upon these generalized invexity,G-Fritz-John （G-F-J） and G-Karnsh-Kuhn-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 G-Mond-Weir type dual under various types of generalized dI-G-type Ⅰ invexity assumptions.展开更多
This paper deals with some problems of multiobjective posynomial geometric programming. AKuhn-Tucker type optimality sufficient condition of this programming is derived. Moreover,a dual problemassociated with multiobj...This paper deals with some problems of multiobjective posynomial geometric programming. AKuhn-Tucker type optimality sufficient condition of this programming is derived. Moreover,a dual problemassociated with multiobjective posynomial geometric programming is given, and weak duality,direct dualityand inverse duality theorems are proved.展开更多
First, a class of higher order exponential type hybrid （α,β, γ, η, p, h（.,.）, κ（., .）, w（.,., .）, ω（.,.,.）, θ）-invexities is introduced, second, some parametrically sufficient efficiency conditions ba...First, a class of higher order exponential type hybrid （α,β, γ, η, p, h（.,.）, κ（., .）, w（.,., .）, ω（.,.,.）, θ）-invexities is introduced, second, some parametrically sufficient efficiency conditions based on the higher order exponential type hybrid invexities are established, and finally some parametrically sufficient efficiency results under the higher order exponential type hybrid （a,β, γ, ρ, h（.,.）, k（.,-）, w（-,., .）, w（.,., .）, 0）-invexities are investigated to the context of solving semiinfinite multiobjective fractional programming problems. The notions of the higher order exponential type hybrid （a, β, γ η, p, h（., .）, n（., .）, w（-,.,-）, ω（.,.,.）, 0）-invexities encompass most of the generalized invexities in the literature. To the best of our knowledge, the results on semiinfinite multiobjective fractional programming problems established in this communication are new and application-oriented toward multitime multi- objectve problems as well as multiobiective control problems.展开更多
In this paper we generalize the concept of a Dini-convex function with Dini derivative and introduce a new concept - Dini-invexity. Some properties of Diniinvex functions are discussed. On the base of this, we study t...In this paper we generalize the concept of a Dini-convex function with Dini derivative and introduce a new concept - Dini-invexity. Some properties of Diniinvex functions are discussed. On the base of this, we study the Wolfe type duality and Mond-Weir type duality for Dini-invex nonsmooth multiobjective programmings and obtain corresponding duality theorems.展开更多
This paper considers multiobjective integer programming problems involving random variables in constraints. Using the concept of simple recourse, the formulated multiobjective stochastic simple recourse problems are t...This paper considers multiobjective integer programming problems involving random variables in constraints. Using the concept of simple recourse, the formulated multiobjective stochastic simple recourse problems are transformed into deterministic ones. For solving transformed deterministic problems efficiently, we also introduce genetic algorithms with double strings for nonlinear integer programming problems. Taking into account vagueness of judgments of the decision maker, an interactive fuzzy satisficing method is presented. In the proposed interactive method, after determineing the fuzzy goals of the decision maker, a satisficing solution for the decision maker is derived efficiently by updating the reference membership levels of the decision maker. An illustrative numerical example is provided to demonstrate the feasibility and efficiency of the proposed method.展开更多
In this paper, we introduce a new class of generalized dI-univexity in which each component of the objective and constraint functions is directionally differentiable in its own direction di for a nondifferentiable mul...In this paper, we introduce a new class of generalized dI-univexity in which each component of the objective and constraint functions is directionally differentiable in its own direction di for a nondifferentiable multiobjective programming problem. Based upon these generalized functions, sufficient optimality conditions are established for a feasible point to be efficient and properly efficient under the generalised dI-univexity requirements. Moreover, weak, strong and strict converse duality theorems are also derived for Mond-Weir type dual programs.展开更多
基金financially supported by Ministerio de Ciencia e Innovación projects SAF2017-82736-C2-1-R to MTMFin Universidad Autónoma de Madrid and by Fundación Universidad Francisco de Vitoria to JS+2 种基金a predoctoral scholarship from Fundación Universidad Francisco de Vitoriafinancial support from a 6-month contract from Universidad Autónoma de Madrida 3-month contract from the School of Medicine of Universidad Francisco de Vitoria。
文摘Every year, around the world, between 250,000 and 500,000 people suffer a spinal cord injury(SCI). SCI is a devastating medical condition that arises from trauma or disease-induced damage to the spinal cord, disrupting the neural connections that allow communication between the brain and the rest of the body, which results in varying degrees of motor and sensory impairment. Disconnection in the spinal tracts is an irreversible condition owing to the poor capacity for spontaneous axonal regeneration in the affected neurons.
基金supported by the National Natural Sci‐ence Foundation of China(Grant No.62306325)。
文摘During the use of robotics in applications such as antiterrorism or combat,a motion-constrained pursuer vehicle,such as a Dubins unmanned surface vehicle(USV),must get close enough(within a prescribed zero or positive distance)to a moving target as quickly as possible,resulting in the extended minimum-time intercept problem(EMTIP).Existing research has primarily focused on the zero-distance intercept problem,MTIP,establishing the necessary or sufficient conditions for MTIP optimality,and utilizing analytic algorithms,such as root-finding algorithms,to calculate the optimal solutions.However,these approaches depend heavily on the properties of the analytic algorithm,making them inapplicable when problem settings change,such as in the case of a positive effective range or complicated target motions outside uniform rectilinear motion.In this study,an approach employing a high-accuracy and quality-guaranteed mixed-integer piecewise-linear program(QG-PWL)is proposed for the EMTIP.This program can accommodate different effective interception ranges and complicated target motions(variable velocity or complicated trajectories).The high accuracy and quality guarantees of QG-PWL originate from elegant strategies such as piecewise linearization and other developed operation strategies.The approximate error in the intercept path length is proved to be bounded to h^(2)/(4√2),where h is the piecewise length.
文摘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.
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National Natural Science Foundation of China(No.11071110)
文摘A new concept of(Φ,ρ,α)-V-invexity for differentiable vector-valued functions is introduced,which is a generalization of differentiable scalar-valued(Φ,ρ)-invexity.Based upon the(Φ,ρ,α)-V-invex functions,sufficient optimality conditions and MondWeir type dual theorems are derived for a class of nondifferentiable multiobjective fractional programming problems in which every component of the objective function and each constraint function contain a term involving the support function of a compact convex set.
基金Foundation item： Supported by the National Natural Science Foundation of China（70071026）
文摘This paper deals with the connectedness of the cone-efficient solution set for vector optimization in locally convex Hausdorff topological vector spaces. The connectedness of the cone-efficient solution set is proved for multiobjective programming defined by a continuous one-to-one cone-quasiconvex mapping on a compact convex set of alternatives. During the proof, the generalized saddle theorem plays a key role.
基金Supported by the National Natural Science Foundation of China(19871009)
文摘In this paper, optimality conditions for multiobjective programming problems having V-invex objective and constraint functions are considered. An equivalent multiobjective programming problem is constructed by a modification of the objective function.Furthermore, a (α, η)-Lagrange function is introduced for a constructed multiobjective programming problem, and a new type of saddle point is introduced. Some results for the new type of saddle point are given.
基金Supported by Chongqing Key Lab. of Operations Research and System Engineering
文摘This paper studies a class of multiobjective generalized fractional programming problems, where the numerators of objective functions are the sum of differentiable function and convex function, while the denominators are the difference of differentiable function and convex function. Under the assumption of Calmness Constraint Qualification the Kuhn-Tucker type necessary conditions for efficient solution are given, and the Kuhn-Tucker type sufficient conditions for efficient solution are presented under the assumptions of （F, α, ρ, d）-V-convexity. Subsequently, the optimality conditions for two kinds of duality models are formulated and duality theorems are proved.
基金Supported by the National Natural Science Foundation of China(Grant No.11171250)
文摘For a multiobjective bilevel programnfing problem （P） with an extremal-value function, its dual problem is constructed by using the Fenchel-Moreau conjugate of the functions involved. Under some convexity and monotonicity assumptions, the weak and strong duality assertions are obtained.
文摘In this paper, we obtain some other properties of the majorly efficient points and solutions of the multiobjective optimization presellted in two previous papers of Hu. By decomposing the major cone, which is non-pointed, non-convex and non-closed into a finite union of disjoint strictly supported pointed convex cones, we discuss the continuous perturbations of the decision space. Several sufficient conditions for the continuity of the sets of majorly efficiellt points and solutions are given.
文摘Multiple objective stochastic linear programming is a relevant topic. As a matter of fact, many practical problems ranging from portfolio selection to water resource management may be cast into this framework. Severe limitations on objectivity are encountered in this field because of the simultaneous presence of randomness and conflicting goals. In such a turbulent environment, the mainstay of rational choice cannot hold and it is virtually impossible to provide a truly scientific foundation for an optimal decision. In this paper, we resort to the bounded rationality principle to introduce satisfying solution for multiobjective stochastic linear programming problems. These solutions that are based on the chance-constrained paradigm are characterized under the assumption of normality of involved random variables. Ways for singling out such solutions are also discussed and a numerical example provided for the sake of illustration.
文摘This study addresses bilevel linear multi-objective problem issues i.e the special case of bilevel linear programming problems where each decision maker has several objective functions conflicting with each other. We introduce an artificial multi-objective linear programming problem of which resolution can permit to generate the whole feasible set of the upper level decisions. Based on this result and depending if the leader can evaluate or not his preferences for his different objective functions, two approaches for obtaining Pareto- optimal solutions are presented.
文摘In this paper, two duality results are established under generalized ρ-convexity conditions for a class of multiobjective fractional programmign involvign differentiable n-sten functions.
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 dI-G-type Ⅰ invexity were introduced for nondifferentiable multiobjective programming problems.Based upon these generalized invexity,G-Fritz-John （G-F-J） and G-Karnsh-Kuhn-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 G-Mond-Weir type dual under various types of generalized dI-G-type Ⅰ invexity assumptions.
文摘This paper deals with some problems of multiobjective posynomial geometric programming. AKuhn-Tucker type optimality sufficient condition of this programming is derived. Moreover,a dual problemassociated with multiobjective posynomial geometric programming is given, and weak duality,direct dualityand inverse duality theorems are proved.
文摘First, a class of higher order exponential type hybrid （α,β, γ, η, p, h（.,.）, κ（., .）, w（.,., .）, ω（.,.,.）, θ）-invexities is introduced, second, some parametrically sufficient efficiency conditions based on the higher order exponential type hybrid invexities are established, and finally some parametrically sufficient efficiency results under the higher order exponential type hybrid （a,β, γ, ρ, h（.,.）, k（.,-）, w（-,., .）, w（.,., .）, 0）-invexities are investigated to the context of solving semiinfinite multiobjective fractional programming problems. The notions of the higher order exponential type hybrid （a, β, γ η, p, h（., .）, n（., .）, w（-,.,-）, ω（.,.,.）, 0）-invexities encompass most of the generalized invexities in the literature. To the best of our knowledge, the results on semiinfinite multiobjective fractional programming problems established in this communication are new and application-oriented toward multitime multi- objectve problems as well as multiobiective control problems.
文摘In this paper we generalize the concept of a Dini-convex function with Dini derivative and introduce a new concept - Dini-invexity. Some properties of Diniinvex functions are discussed. On the base of this, we study the Wolfe type duality and Mond-Weir type duality for Dini-invex nonsmooth multiobjective programmings and obtain corresponding duality theorems.
文摘This paper considers multiobjective integer programming problems involving random variables in constraints. Using the concept of simple recourse, the formulated multiobjective stochastic simple recourse problems are transformed into deterministic ones. For solving transformed deterministic problems efficiently, we also introduce genetic algorithms with double strings for nonlinear integer programming problems. Taking into account vagueness of judgments of the decision maker, an interactive fuzzy satisficing method is presented. In the proposed interactive method, after determineing the fuzzy goals of the decision maker, a satisficing solution for the decision maker is derived efficiently by updating the reference membership levels of the decision maker. An illustrative numerical example is provided to demonstrate the feasibility and efficiency of the proposed method.
文摘In this paper, we introduce a new class of generalized dI-univexity in which each component of the objective and constraint functions is directionally differentiable in its own direction di for a nondifferentiable multiobjective programming problem. Based upon these generalized functions, sufficient optimality conditions are established for a feasible point to be efficient and properly efficient under the generalised dI-univexity requirements. Moreover, weak, strong and strict converse duality theorems are also derived for Mond-Weir type dual programs.
