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
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.
This article is concerned with second-order necessary and sufficient optimality conditions for optimal control problems governed by 3-dimensional Navier-Stokes equations. The periodic state constraint is considered.
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 studies singular optimal control problems for systems described by nonlinear-controlled stochastic differential equations of mean-field type(MFSDEs in short),in which the coefficients depend on the state of...This paper studies singular optimal control problems for systems described by nonlinear-controlled stochastic differential equations of mean-field type(MFSDEs in short),in which the coefficients depend on the state of the solution process as well as of its expected value.Moreover,the cost functional is also of mean-field type.The control variable has two components,the first being absolutely continuous and the second singular.We establish necessary as well as sufficient conditions for optimal singular stochastic control where the system evolves according to MFSDEs.These conditions of optimality differs from the classical one in the sense that here the adjoint equation turns out to be a linear mean-field backward stochastic differential equation.The proof of our result is based on convex perturbation method of a given optimal control.The control domain is assumed to be convex.A linear quadratic stochastic optimal control problem of mean-field type is discussed as an illustrated example.展开更多
In this paper, nonsmooth univex, nonsmooth quasiunivex, and nonsmooth pseudounivex functions are introduced. By utilizing these new concepts, sufficient optimality conditions for a weakly efficient solution of the non...In this paper, nonsmooth univex, nonsmooth quasiunivex, and nonsmooth pseudounivex functions are introduced. By utilizing these new concepts, sufficient optimality conditions for a weakly efficient solution of the nonsmooth multiobjective programming problem are established. Weak and strong duality theorems axe also derived for Mond-Weir type multiobjective dual programs.展开更多
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.
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.
基金This work was supported by National Natural Science Foundation of China (10401041)Natural Science Foundation of Hubei Province (2004ABA009)
文摘This article is concerned with second-order necessary and sufficient optimality conditions for optimal control problems governed by 3-dimensional Navier-Stokes equations. The periodic state constraint is considered.
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.
基金The authorwould like to thank the editor,the associate editor,and anonymous referees for their constructive corrections and valuable suggestions that improved the manuscript.The author was partially supported by Algerian PNR Project Grant 08/u07/857,ATRST-(ANDRU)2011-2013.
文摘This paper studies singular optimal control problems for systems described by nonlinear-controlled stochastic differential equations of mean-field type(MFSDEs in short),in which the coefficients depend on the state of the solution process as well as of its expected value.Moreover,the cost functional is also of mean-field type.The control variable has two components,the first being absolutely continuous and the second singular.We establish necessary as well as sufficient conditions for optimal singular stochastic control where the system evolves according to MFSDEs.These conditions of optimality differs from the classical one in the sense that here the adjoint equation turns out to be a linear mean-field backward stochastic differential equation.The proof of our result is based on convex perturbation method of a given optimal control.The control domain is assumed to be convex.A linear quadratic stochastic optimal control problem of mean-field type is discussed as an illustrated example.
基金supported by the National Natural Science Foundation of China under Grant No.11001287the Natural Science Foundation Project of Chongqing(CSTC 2010BB9254)the Education Committee Project Research Foundation of Chongqing under Grant No.KJ100711
文摘In this paper, nonsmooth univex, nonsmooth quasiunivex, and nonsmooth pseudounivex functions are introduced. By utilizing these new concepts, sufficient optimality conditions for a weakly efficient solution of the nonsmooth multiobjective programming problem are established. Weak and strong duality theorems axe also derived for Mond-Weir type multiobjective dual programs.
