The purpose of this paper is to define the concept of mixed saddle point for a vector-valued Lagrangian of the non-smooth multiobjective vector-valued constrained optimization problem and establish the equivalence of ...The purpose of this paper is to define the concept of mixed saddle point for a vector-valued Lagrangian of the non-smooth multiobjective vector-valued constrained optimization problem and establish the equivalence of the mixed saddle point and an efficient solution under generalized (V, p)-invexity assumptions.展开更多
The aim of this paper is to study the relationship among Minty vector variational-like inequality problem, Stampacchia vector variational-like inequality problem and vector optimization problem involving (G, α)-invex...The aim of this paper is to study the relationship among Minty vector variational-like inequality problem, Stampacchia vector variational-like inequality problem and vector optimization problem involving (G, α)-invex functions. Furthermore, we establish equivalence among the solutions of weak formulations of Minty vector variational-like inequality problem, Stampacchia vector variational-like inequality problem and weak efficient solution of vector optimization problem under the assumption of (G, α)-invex functions. Examples are provided to elucidate our results.展开更多
In the present paper the definition of invexity for continuous functions is extended to invexity of order m which is further generalized to ρ-pseudoinvexity type I of order m, ρ-pseudoinvexity type II of order m, as...In the present paper the definition of invexity for continuous functions is extended to invexity of order m which is further generalized to ρ-pseudoinvexity type I of order m, ρ-pseudoinvexity type II of order m, as well as ρ-quasi invexity type I of order m and ρ-quasiinvexity type II of order m. The central objective of the paper is to study variational problem where the functionals involved satisfy the above stated generalized ρ-invexity assumptions of order m. Wolfe type and Mond Weir type of duals are formulated. Sufficient optimality conditions and duality results are proved. It is demonstrated with the help of an example that the class of ρ-invex functionals of order m is more general than the class of ρ-invex functionals. Further, it may be noted that the results presented in this paper are more powerful than the existing results as this new class of functions defined here satisfies mth derivative test.展开更多
Minimax programming problems involving generalized （p, r）-invex functions are consid- ered. Parametric sufficient optimality conditions and duality results are established under the aforesaid assumptions on the obje...Minimax programming problems involving generalized （p, r）-invex functions are consid- ered. Parametric sufficient optimality conditions and duality results are established under the aforesaid assumptions on the objective and constraint functions.展开更多
In this paper,we emphasize on a nondifferentiable minimax fractional programming(NMFP)problem and obtain appropriate duality results for higher-order dual model under higher-order B-(p,r)-invex functions.We provide a ...In this paper,we emphasize on a nondifferentiable minimax fractional programming(NMFP)problem and obtain appropriate duality results for higher-order dual model under higher-order B-(p,r)-invex functions.We provide a nontrivial illustration of a function which belongs to the class of higher-order B-(p,r)-invex but not in the class of second-order B-(p,r)-invex functions already existing in literature.An example of finding a minimax solution of NMFP problem by using higher-order B-(p,r)-invex functions has also been given.Various known results are discussed as particular cases.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
The purpose of this paper is to devise exact l_(1) exponential penalty function method to solve multiobjective optimization problems with exponentialtype invexity.The conditions governing the equivalence of the(weak)...The purpose of this paper is to devise exact l_(1) exponential penalty function method to solve multiobjective optimization problems with exponentialtype invexity.The conditions governing the equivalence of the(weak)efficient solutions to the vector optimization problem and the(weak)efficient solutions to associated unconstrained exponential penalized multiobjective optimization problem are studied.Examples are given to illustrate the obtained results.展开更多
文摘The purpose of this paper is to define the concept of mixed saddle point for a vector-valued Lagrangian of the non-smooth multiobjective vector-valued constrained optimization problem and establish the equivalence of the mixed saddle point and an efficient solution under generalized (V, p)-invexity assumptions.
文摘The aim of this paper is to study the relationship among Minty vector variational-like inequality problem, Stampacchia vector variational-like inequality problem and vector optimization problem involving (G, α)-invex functions. Furthermore, we establish equivalence among the solutions of weak formulations of Minty vector variational-like inequality problem, Stampacchia vector variational-like inequality problem and weak efficient solution of vector optimization problem under the assumption of (G, α)-invex functions. Examples are provided to elucidate our results.
文摘In the present paper the definition of invexity for continuous functions is extended to invexity of order m which is further generalized to ρ-pseudoinvexity type I of order m, ρ-pseudoinvexity type II of order m, as well as ρ-quasi invexity type I of order m and ρ-quasiinvexity type II of order m. The central objective of the paper is to study variational problem where the functionals involved satisfy the above stated generalized ρ-invexity assumptions of order m. Wolfe type and Mond Weir type of duals are formulated. Sufficient optimality conditions and duality results are proved. It is demonstrated with the help of an example that the class of ρ-invex functionals of order m is more general than the class of ρ-invex functionals. Further, it may be noted that the results presented in this paper are more powerful than the existing results as this new class of functions defined here satisfies mth derivative test.
文摘Minimax programming problems involving generalized （p, r）-invex functions are consid- ered. Parametric sufficient optimality conditions and duality results are established under the aforesaid assumptions on the objective and constraint functions.
文摘In this paper,we emphasize on a nondifferentiable minimax fractional programming(NMFP)problem and obtain appropriate duality results for higher-order dual model under higher-order B-(p,r)-invex functions.We provide a nontrivial illustration of a function which belongs to the class of higher-order B-(p,r)-invex but not in the class of second-order B-(p,r)-invex functions already existing in literature.An example of finding a minimax solution of NMFP problem by using higher-order B-(p,r)-invex functions has also been given.Various known results are discussed as particular cases.
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.
基金The research of the first author is financially supported by the University Grant Commission,New Delhi,India(No.41-801/2012(SR)).
文摘The purpose of this paper is to devise exact l_(1) exponential penalty function method to solve multiobjective optimization problems with exponentialtype invexity.The conditions governing the equivalence of the(weak)efficient solutions to the vector optimization problem and the(weak)efficient solutions to associated unconstrained exponential penalized multiobjective optimization problem are studied.Examples are given to illustrate the obtained results.
