In this paper, the so-called approximate convexity and concavity properties of generalized Groetzsch ring function μa （r） by studying the monotonieity,convexity or concavity of certain composites of μa（r） are ob...In this paper, the so-called approximate convexity and concavity properties of generalized Groetzsch ring function μa （r） by studying the monotonieity,convexity or concavity of certain composites of μa（r） are obtained.展开更多
Based on the ordering of fuzzy numbers proposed by Goetschel and Voxman,the representations and some properties of strongly preinvex fuzzy-valued function are defined and obtained, several new concepts of strongly mon...Based on the ordering of fuzzy numbers proposed by Goetschel and Voxman,the representations and some properties of strongly preinvex fuzzy-valued function are defined and obtained, several new concepts of strongly monotonicities fuzzy functions are introduced, the relationship among the strongly preinvex, strongly invex and monotonicities under some suitable and appropriate conditions is established and a necessary condition for strongly pseudoinvex functions is given. As an application, the conditions of local optimal solution and global optimal solution in the mathematical programming problem are discussed.展开更多
In this paper,the authors study the monotoneity and convexity of certain combinations and composites defined in terms of the generalized Grotzsch ring function μa (r), which appears in Ramanujan' s generalized mo...In this paper,the authors study the monotoneity and convexity of certain combinations and composites defined in terms of the generalized Grotzsch ring function μa (r), which appears in Ramanujan' s generalized modular equations,and obtain some inequalities for this function.展开更多
Hanson and Mond have grven sets of necessary and sufficient conditions for optimality in constrained optimization by introducing classes of generalized functions, called type Ⅰ functions. Recently, Bector definded un...Hanson and Mond have grven sets of necessary and sufficient conditions for optimality in constrained optimization by introducing classes of generalized functions, called type Ⅰ functions. Recently, Bector definded univex functions, a new class of functions that unifies several concepts of generalized convexity. In this paper, additional conditions are attached to the Kuhn Tucker conditions giving a set of conditions which are both necessary and sufficient for optimality in constrained optimization, under appropriate constraint qualifications.展开更多
We establish the monotonicity and convexity properties for several special functions involving the generalized elliptic integrals, and present some new analytic inequalities.
The properties of generalized convexity are studied in this paper,as well as an existence Theorem of solutions for a type of generalized quasi-variational inequality is then abtained.
In this paper, another form of KKM type theorem on generalized convex spaces is obtained and the problems of von Neumann-Fan type sup inf sup inequalities and variational inequalities are discussed for their applicati...In this paper, another form of KKM type theorem on generalized convex spaces is obtained and the problems of von Neumann-Fan type sup inf sup inequalities and variational inequalities are discussed for their applications.The main results improve and generalize the corresponding results in previous papers.展开更多
In this paper we investigate generalized bi quasi variational inequalities in locally convex topological vector spaces. Motivated and inspired by the recent research work in this field,we establish several existence t...In this paper we investigate generalized bi quasi variational inequalities in locally convex topological vector spaces. Motivated and inspired by the recent research work in this field,we establish several existence theorems of solutions for generalized bi quasi variational inequalities,which are the extension and improvements of the earlier and recent results obtained previously by many authors including Sun and Ding [18],Chang and Zhang [23] and Zhang [24].展开更多
In this paper,we offer a new sparse recovery strategy based on the generalized error function.The introduced penalty function involves both the shape and the scale parameters,making it extremely flexible.For both cons...In this paper,we offer a new sparse recovery strategy based on the generalized error function.The introduced penalty function involves both the shape and the scale parameters,making it extremely flexible.For both constrained and unconstrained models,the theoretical analysis results in terms of the null space property,the spherical section property and the restricted invertibility factor are established.The practical algorithms via both the iteratively reweighted■_(1)and the difference of convex functions algorithms are presented.Numerical experiments are carried out to demonstrate the benefits of the suggested approach in a variety of circumstances.Its practical application in magnetic resonance imaging(MRI)reconstruction is also investigated.展开更多
The aim of this paper is to prove that the average function of a trigonometrically ρ-convex function is trigonometrically ρ-convex. Furthermore, we show the existence of support curves implies the trigonometric ρ-c...The aim of this paper is to prove that the average function of a trigonometrically ρ-convex function is trigonometrically ρ-convex. Furthermore, we show the existence of support curves implies the trigonometric ρ-convexity, and prove an extremum property of this function.展开更多
In this paper, we define the concepts of (η,h)-quasi pseudo-monotone operators on compact set in locally convex Hausdorff topological vector spaces and prove the existence results of solutions for a class of generali...In this paper, we define the concepts of (η,h)-quasi pseudo-monotone operators on compact set in locally convex Hausdorff topological vector spaces and prove the existence results of solutions for a class of generalized quasi variational type inequalities in locally convex Hausdorff topological vector spaces.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
Mond-Weir type duality for control problem with support functions is investigated under generalized convexity conditions. Special cases are derived. A relationship between our results and those of nonlinear programmin...Mond-Weir type duality for control problem with support functions is investigated under generalized convexity conditions. Special cases are derived. A relationship between our results and those of nonlinear programming problem containing support functions is outlined.展开更多
A control problem containing support functions in the integrand of the objective of the functional as well as in the inequality constraint function is considered. For this problem, Fritz John and Karush-Kuhn-Tucker ty...A control problem containing support functions in the integrand of the objective of the functional as well as in the inequality constraint function is considered. For this problem, Fritz John and Karush-Kuhn-Tucker type necessary optimality conditions are derived. Using Karush-Kuhn-Tucker type optimality conditions, Wolfe type dual is formulated and usual duality theorems are established under generalized convexity conditions. Special cases are generated. It is also shown that our duality results have linkage with those of nonlinear programming problems involving support functions.展开更多
This paper extends the class of generalized type I functions introduced by Aghezzaf and Hachimi（2000） to the context of higher-order case and formulate a number of higher-order duals to a non-differentiable multi-ob...This paper extends the class of generalized type I functions introduced by Aghezzaf and Hachimi（2000） to the context of higher-order case and formulate a number of higher-order duals to a non-differentiable multi-objective programming problem and establishes higher-order duality results under the higher-order generalized type I functions introduced in the present paper, A special case that appears repeatedly in the literature is that the support function is the square root of a positive semi-definite quadratic form. This and other special cases can be readily generated from these results.展开更多
A class of functions and a sort of nonlinear programming called respectively E-convex functions and E-convex programming were presented and studied recently by Youness in [1], In this paper, we point out the most resu...A class of functions and a sort of nonlinear programming called respectively E-convex functions and E-convex programming were presented and studied recently by Youness in [1], In this paper, we point out the most results for .E-convex functions and E-convex programming in [1] are not true by six counter examples.展开更多
文摘In this paper, the so-called approximate convexity and concavity properties of generalized Groetzsch ring function μa （r） by studying the monotonieity,convexity or concavity of certain composites of μa（r） are obtained.
基金Supported by Natural Science Foundation of Gansu Province of China (Grant No.18JR3RM238)Research Foundation of Higher Education of Gansu Province of China (Grant No. 2018A-101)Innovation Ability promotion Project of Higher Education of Gansu Province of China (Grant No. 2019A-117)。
文摘Based on the ordering of fuzzy numbers proposed by Goetschel and Voxman,the representations and some properties of strongly preinvex fuzzy-valued function are defined and obtained, several new concepts of strongly monotonicities fuzzy functions are introduced, the relationship among the strongly preinvex, strongly invex and monotonicities under some suitable and appropriate conditions is established and a necessary condition for strongly pseudoinvex functions is given. As an application, the conditions of local optimal solution and global optimal solution in the mathematical programming problem are discussed.
文摘In this paper,the authors study the monotoneity and convexity of certain combinations and composites defined in terms of the generalized Grotzsch ring function μa (r), which appears in Ramanujan' s generalized modular equations,and obtain some inequalities for this function.
文摘Hanson and Mond have grven sets of necessary and sufficient conditions for optimality in constrained optimization by introducing classes of generalized functions, called type Ⅰ functions. Recently, Bector definded univex functions, a new class of functions that unifies several concepts of generalized convexity. In this paper, additional conditions are attached to the Kuhn Tucker conditions giving a set of conditions which are both necessary and sufficient for optimality in constrained optimization, under appropriate constraint qualifications.
基金supported by the Natural Science Foundation of China(11701176,61673169,11301127,11626101,11601485)the Science and Technology Research Program of Zhejiang Educational Committee(Y201635325)
文摘We establish the monotonicity and convexity properties for several special functions involving the generalized elliptic integrals, and present some new analytic inequalities.
文摘The properties of generalized convexity are studied in this paper,as well as an existence Theorem of solutions for a type of generalized quasi-variational inequality is then abtained.
文摘In this paper, another form of KKM type theorem on generalized convex spaces is obtained and the problems of von Neumann-Fan type sup inf sup inequalities and variational inequalities are discussed for their applications.The main results improve and generalize the corresponding results in previous papers.
文摘In this paper we investigate generalized bi quasi variational inequalities in locally convex topological vector spaces. Motivated and inspired by the recent research work in this field,we establish several existence theorems of solutions for generalized bi quasi variational inequalities,which are the extension and improvements of the earlier and recent results obtained previously by many authors including Sun and Ding [18],Chang and Zhang [23] and Zhang [24].
基金supported by the Zhejiang Provincial Natural Science Foundation of China under grant No.LQ21A010003.
文摘In this paper,we offer a new sparse recovery strategy based on the generalized error function.The introduced penalty function involves both the shape and the scale parameters,making it extremely flexible.For both constrained and unconstrained models,the theoretical analysis results in terms of the null space property,the spherical section property and the restricted invertibility factor are established.The practical algorithms via both the iteratively reweighted■_(1)and the difference of convex functions algorithms are presented.Numerical experiments are carried out to demonstrate the benefits of the suggested approach in a variety of circumstances.Its practical application in magnetic resonance imaging(MRI)reconstruction is also investigated.
文摘The aim of this paper is to prove that the average function of a trigonometrically ρ-convex function is trigonometrically ρ-convex. Furthermore, we show the existence of support curves implies the trigonometric ρ-convexity, and prove an extremum property of this function.
文摘In this paper, we define the concepts of (η,h)-quasi pseudo-monotone operators on compact set in locally convex Hausdorff topological vector spaces and prove the existence results of solutions for a class of generalized quasi variational type inequalities in locally convex Hausdorff topological vector spaces.
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.
文摘Mond-Weir type duality for control problem with support functions is investigated under generalized convexity conditions. Special cases are derived. A relationship between our results and those of nonlinear programming problem containing support functions is outlined.
文摘A control problem containing support functions in the integrand of the objective of the functional as well as in the inequality constraint function is considered. For this problem, Fritz John and Karush-Kuhn-Tucker type necessary optimality conditions are derived. Using Karush-Kuhn-Tucker type optimality conditions, Wolfe type dual is formulated and usual duality theorems are established under generalized convexity conditions. Special cases are generated. It is also shown that our duality results have linkage with those of nonlinear programming problems involving support functions.
文摘This paper extends the class of generalized type I functions introduced by Aghezzaf and Hachimi（2000） to the context of higher-order case and formulate a number of higher-order duals to a non-differentiable multi-objective programming problem and establishes higher-order duality results under the higher-order generalized type I functions introduced in the present paper, A special case that appears repeatedly in the literature is that the support function is the square root of a positive semi-definite quadratic form. This and other special cases can be readily generated from these results.
基金National Natural Science Foundation of China(10261001)Science Foundation of Guangxi(0236001)
文摘A class of functions and a sort of nonlinear programming called respectively E-convex functions and E-convex programming were presented and studied recently by Youness in [1], In this paper, we point out the most results for .E-convex functions and E-convex programming in [1] are not true by six counter examples.
