The concepts of alpha-order Clarke's derivative, alpha-order Adjacent derivative and alpha-order G.Bouligand derivative of set-valued mappings are introduced, their properties are studied, with which the Fritz Joh...The concepts of alpha-order Clarke's derivative, alpha-order Adjacent derivative and alpha-order G.Bouligand derivative of set-valued mappings are introduced, their properties are studied, with which the Fritz John optimality condition of set-valued vector optimization is established. Finally, under the assumption of pseudoconvexity, the optimality condition is proved to be sufficient.展开更多
In locally convex Hausdorff topological vector spaces,ε-strongly efficient solutions for vector optimization with set-valued maps are discussed.Firstly,ε-strongly efficient point of set is introduced.Secondly,under ...In locally convex Hausdorff topological vector spaces,ε-strongly efficient solutions for vector optimization with set-valued maps are discussed.Firstly,ε-strongly efficient point of set is introduced.Secondly,under the nearly cone-subconvexlike set-valued maps,the theorem of scalarization for vector optimization is obtained.Finally,optimality conditions of ε-strongly efficient solutions for vector optimization with generalized inequality constraints and equality constraints are obtained.展开更多
采用正交设计法对磷酸铵镁(MAP)的生成进行了研究。方差分析结果表明:在MAP晶体的形成过程中,溶液的pH值、初始P浓度(C_(0)),以及二者的交互作用是MAP形成的显著性因素,对MAP的形成起决定性作用。依据各因素K值的大小,确定了MAP生成工...采用正交设计法对磷酸铵镁(MAP)的生成进行了研究。方差分析结果表明:在MAP晶体的形成过程中,溶液的pH值、初始P浓度(C_(0)),以及二者的交互作用是MAP形成的显著性因素,对MAP的形成起决定性作用。依据各因素K值的大小,确定了MAP生成工艺的最优方案为A_(3)B_(3)C_(3)D_(2)E_(1)F_(2)。在最优方案条件下,制备获得2.241 g MAP晶体。SEM扫描谱图显示:沉淀物的主要成分为磷酸铵镁晶体。展开更多
In this paper, firstly, a new notion of generalized cone convex set-valued map is introduced in real normed spaces. Secondly, a property of the generalized cone convex set-valued map involving the contingent epideriva...In this paper, firstly, a new notion of generalized cone convex set-valued map is introduced in real normed spaces. Secondly, a property of the generalized cone convex set-valued map involving the contingent epiderivative is obtained. Finally, as the applications of this property, we use the contingent epiderivative to establish optimality conditions of the set-valued optimization problem with generalized cone convex set-valued maps in the sense of Henig proper efficiency. The results obtained in this paper generalize and improve some known results in the literature.展开更多
The convergence analysis of a nonlinear Lagrange algorithm for solving nonlinear constrained optimization problems with both inequality and equality constraints is explored in detail. The estimates for the derivatives...The convergence analysis of a nonlinear Lagrange algorithm for solving nonlinear constrained optimization problems with both inequality and equality constraints is explored in detail. The estimates for the derivatives of the multiplier mapping and the solution mapping of the proposed algorithm are discussed via the technique of the singular value decomposition of matrix. Based on the estimates, the local convergence results and the rate of convergence of the algorithm are presented when the penalty parameter is less than a threshold under a set of suitable conditions on problem functions. Furthermore, the condition number of the Hessian of the nonlinear Lagrange function with respect to the decision variables is analyzed, which is closely related to efficiency of the algorithm. Finally, the preliminary numericM results for several typical test problems are reported.展开更多
The concept of a cone subarcwise connected set-valued map is introduced. Several examples are given to illustrate that the cone subarcwise connected set-valued map is a proper generalization of the cone arcwise connec...The concept of a cone subarcwise connected set-valued map is introduced. Several examples are given to illustrate that the cone subarcwise connected set-valued map is a proper generalization of the cone arcwise connected set-valued map, as well as the arcwise connected set is a proper generalization of the convex set,respectively. Then, by virtue of the generalized second-order contingent epiderivative, second-order necessary optimality conditions are established for a point pair to be a local global proper efficient element of set-valued optimization problems. When objective function is cone subarcwise connected, a second-order sufficient optimality condition is also obtained for a point pair to be a global proper efficient element of set-valued optimization problems.展开更多
基金the National Natural Science Foundation(69972036) and the Natural Science Foundation of Shanxi province(995L02)
文摘The concepts of alpha-order Clarke's derivative, alpha-order Adjacent derivative and alpha-order G.Bouligand derivative of set-valued mappings are introduced, their properties are studied, with which the Fritz John optimality condition of set-valued vector optimization is established. Finally, under the assumption of pseudoconvexity, the optimality condition is proved to be sufficient.
基金Foundation item： Supported by the Natural Science Foundation of China（10871216） Supported by the Natural Science Foundation Project of CQ CSTC（2008BB0346, 2007BB0441） Supported by the Excellent Young Teachers Program of Chongqing Jiaotong University（EYT08-016） Acknowledgement The author would like to thank the anonymous referee for the valuable remarks that helped considerably to correct and to improve the presentation.
文摘In locally convex Hausdorff topological vector spaces,ε-strongly efficient solutions for vector optimization with set-valued maps are discussed.Firstly,ε-strongly efficient point of set is introduced.Secondly,under the nearly cone-subconvexlike set-valued maps,the theorem of scalarization for vector optimization is obtained.Finally,optimality conditions of ε-strongly efficient solutions for vector optimization with generalized inequality constraints and equality constraints are obtained.
文摘采用正交设计法对磷酸铵镁(MAP)的生成进行了研究。方差分析结果表明:在MAP晶体的形成过程中,溶液的pH值、初始P浓度(C_(0)),以及二者的交互作用是MAP形成的显著性因素,对MAP的形成起决定性作用。依据各因素K值的大小,确定了MAP生成工艺的最优方案为A_(3)B_(3)C_(3)D_(2)E_(1)F_(2)。在最优方案条件下,制备获得2.241 g MAP晶体。SEM扫描谱图显示:沉淀物的主要成分为磷酸铵镁晶体。
基金supported by the National Nature Science Foundation of China(11431004,11471291)the General Project of Chongqing Frontier and Applied Foundation Research(cstc2015jcyj A00050)the Key Project of Chongqing Frontier and Applied Foundation Research(cstc2017jcyj BX0055,cstc2015jcyj BX0113)
文摘In this paper, firstly, a new notion of generalized cone convex set-valued map is introduced in real normed spaces. Secondly, a property of the generalized cone convex set-valued map involving the contingent epiderivative is obtained. Finally, as the applications of this property, we use the contingent epiderivative to establish optimality conditions of the set-valued optimization problem with generalized cone convex set-valued maps in the sense of Henig proper efficiency. The results obtained in this paper generalize and improve some known results in the literature.
基金Supported by the National Natural Science Foundation of China(11201357,81271513 and 91324201)the Fundamental Research Funds for the Central Universities under project(2014-Ia-001)
文摘The convergence analysis of a nonlinear Lagrange algorithm for solving nonlinear constrained optimization problems with both inequality and equality constraints is explored in detail. The estimates for the derivatives of the multiplier mapping and the solution mapping of the proposed algorithm are discussed via the technique of the singular value decomposition of matrix. Based on the estimates, the local convergence results and the rate of convergence of the algorithm are presented when the penalty parameter is less than a threshold under a set of suitable conditions on problem functions. Furthermore, the condition number of the Hessian of the nonlinear Lagrange function with respect to the decision variables is analyzed, which is closely related to efficiency of the algorithm. Finally, the preliminary numericM results for several typical test problems are reported.
基金Supported by the National Natural Science Foundation of China Grant 11461044the Natural Science Foundation of Jiangxi Province(20151BAB201027)the Science and Technology Foundation of the Education Department of Jiangxi Province(GJJ12010)
文摘The concept of a cone subarcwise connected set-valued map is introduced. Several examples are given to illustrate that the cone subarcwise connected set-valued map is a proper generalization of the cone arcwise connected set-valued map, as well as the arcwise connected set is a proper generalization of the convex set,respectively. Then, by virtue of the generalized second-order contingent epiderivative, second-order necessary optimality conditions are established for a point pair to be a local global proper efficient element of set-valued optimization problems. When objective function is cone subarcwise connected, a second-order sufficient optimality condition is also obtained for a point pair to be a global proper efficient element of set-valued optimization problems.
基金Supported by the National Natural Science Foundation of China(10472003)Beijing Natural Science Foundation (3002002)Beijing Educational Committee and the American MSC Company(KM200410005019)
