The D-η-proper prequasi invexity of vector-valued functions is characterized by means of （weak） nearly convexity and density of sets. Under weaker assumptions, some equivalent conditions for D-η-proper prequasi-in...The D-η-proper prequasi invexity of vector-valued functions is characterized by means of （weak） nearly convexity and density of sets. Under weaker assumptions, some equivalent conditions for D-η-proper prequasi-invexity are derived.展开更多
A semi-infinite programming problem is a mathematical programming problem with a finite number of variables and infinitely many constraints. Duality theories and generalized convexity concepts are important research t...A semi-infinite programming problem is a mathematical programming problem with a finite number of variables and infinitely many constraints. Duality theories and generalized convexity concepts are important research topics in mathematical programming. In this paper, we discuss a fairly large number of paramet- ric duality results under various generalized （η,ρ）-invexity assumptions for a semi-infinite minmax fractional programming problem.展开更多
In this paper, we discuss a large number of sets of global parametric sufficient optimality conditions under various generalized （η,ρ）-invexity assumptions for a semi-infinite minmax fractional programming problem.
In this paper, we present several parametric duality results under various generalized （a,v,p）-V- invexity assumptions for a semiinfinite multiobjective fractional programming problem.
Abstract In this paper, we discuss numerous sets of global parametric sufficient efficiency conditions under various generalized （a,n, p）-V-invexity assumptions for a semiinfinite multiobjective fractional programmi...Abstract In this paper, we discuss numerous sets of global parametric sufficient efficiency conditions under various generalized （a,n, p）-V-invexity assumptions for a semiinfinite multiobjective fractional programming problem.展开更多
The exact minimax penalty function method is used to solve a noncon- vex differentiable optimization problem with both inequality and equality constraints. The conditions for exactness of the penalization for the exac...The exact minimax penalty function method is used to solve a noncon- vex differentiable optimization problem with both inequality and equality constraints. The conditions for exactness of the penalization for the exact minimax penalty function method are established by assuming that the functions constituting the considered con- strained optimization problem are invex with respect to the same function η （with the exception of those equality constraints for which the associated Lagrange multipliers are negative these functions should be assumed to be incave with respect to η）. Thus, a threshold of the penalty parameter is given such that, for all penalty parameters exceeding this threshold, equivalence holds between the set of optimal solutions in the considered constrained optimization problem and the set of minimizer in its associated penalized problem with an exact minimax penalty function. It is shown that coercivity is not suf- ficient to prove the results.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 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
In this article, for a differentiable function , we introduce the definition of the higher-order -invexity. Three duality models for a multiobjective fractional programming problem involving nondifferentiability in te...In this article, for a differentiable function , we introduce the definition of the higher-order -invexity. Three duality models for a multiobjective fractional programming problem involving nondifferentiability in terms of support functions have been formulated and usual duality relations have been established under the higher-order -invex assumptions.展开更多
A second-order Mond-Weir type dual problem is formulated for a class of continuous programming problems in which both objective and constraint functions contain support functions;hence it is nondifferentiable. Under s...A second-order Mond-Weir type dual problem is formulated for a class of continuous programming problems in which both objective and constraint functions contain support functions;hence it is nondifferentiable. Under second-order strict pseudoinvexity, second-order pseudoinvexity and second-order quasi-invexity assumptions on functionals, weak, strong, strict converse and converse duality theorems are established for this pair of dual continuous programming problems. Special cases are deduced and a pair of dual continuous problems with natural boundary values is constructed. A close relationship between the duality results of our problems and those of the corresponding (static) nonlinear programming problem with support functions is briefly outlined.展开更多
A second-order dual problem is formulated for a class of continuous programming problem in which both objective and constrained functions contain support functions, hence it is nondifferentiable. Under second-order in...A second-order dual problem is formulated for a class of continuous programming problem in which both objective and constrained functions contain support functions, hence it is nondifferentiable. Under second-order invexity and second-order pseudoinvexity, weak, strong and converse duality theorems are established for this pair of dual problems. Special cases are deduced and a pair of dual continuous problems with natural boundary values is constructed. A close relationship between duality results of our problems and those of the corresponding (static) nonlinear programming problem with support functions is briefly outlined.展开更多
文摘The D-η-proper prequasi invexity of vector-valued functions is characterized by means of （weak） nearly convexity and density of sets. Under weaker assumptions, some equivalent conditions for D-η-proper prequasi-invexity are derived.
文摘A semi-infinite programming problem is a mathematical programming problem with a finite number of variables and infinitely many constraints. Duality theories and generalized convexity concepts are important research topics in mathematical programming. In this paper, we discuss a fairly large number of paramet- ric duality results under various generalized （η,ρ）-invexity assumptions for a semi-infinite minmax fractional programming problem.
文摘In this paper, we discuss a large number of sets of global parametric sufficient optimality conditions under various generalized （η,ρ）-invexity assumptions for a semi-infinite minmax fractional programming problem.
文摘In this paper, we present several parametric duality results under various generalized （a,v,p）-V- invexity assumptions for a semiinfinite multiobjective fractional programming problem.
文摘Abstract In this paper, we discuss numerous sets of global parametric sufficient efficiency conditions under various generalized （a,n, p）-V-invexity assumptions for a semiinfinite multiobjective fractional programming problem.
文摘The exact minimax penalty function method is used to solve a noncon- vex differentiable optimization problem with both inequality and equality constraints. The conditions for exactness of the penalization for the exact minimax penalty function method are established by assuming that the functions constituting the considered con- strained optimization problem are invex with respect to the same function η （with the exception of those equality constraints for which the associated Lagrange multipliers are negative these functions should be assumed to be incave with respect to η）. Thus, a threshold of the penalty parameter is given such that, for all penalty parameters exceeding this threshold, equivalence holds between the set of optimal solutions in the considered constrained optimization problem and the set of minimizer in its associated penalized problem with an exact minimax penalty function. It is shown that coercivity is not suf- ficient to prove the results.
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In this article, for a differentiable function , we introduce the definition of the higher-order -invexity. Three duality models for a multiobjective fractional programming problem involving nondifferentiability in terms of support functions have been formulated and usual duality relations have been established under the higher-order -invex assumptions.
文摘A second-order Mond-Weir type dual problem is formulated for a class of continuous programming problems in which both objective and constraint functions contain support functions;hence it is nondifferentiable. Under second-order strict pseudoinvexity, second-order pseudoinvexity and second-order quasi-invexity assumptions on functionals, weak, strong, strict converse and converse duality theorems are established for this pair of dual continuous programming problems. Special cases are deduced and a pair of dual continuous problems with natural boundary values is constructed. A close relationship between the duality results of our problems and those of the corresponding (static) nonlinear programming problem with support functions is briefly outlined.
文摘A second-order dual problem is formulated for a class of continuous programming problem in which both objective and constrained functions contain support functions, hence it is nondifferentiable. Under second-order invexity and second-order pseudoinvexity, weak, strong and converse duality theorems are established for this pair of dual problems. Special cases are deduced and a pair of dual continuous problems with natural boundary values is constructed. A close relationship between duality results of our problems and those of the corresponding (static) nonlinear programming problem with support functions is briefly outlined.
