In this paper,the ε-super effcient solution for set-valued map vector optimization in locally convex space is introduced.And under the assumption of the nearly generalized cone-subconvexlikeness for set-valued maps,u...In this paper,the ε-super effcient solution for set-valued map vector optimization in locally convex space is introduced.And under the assumption of the nearly generalized cone-subconvexlikeness for set-valued maps,used new methods,the scalarization theorem and Lagrange multiplier theorem for ε-super effcient solution are established.展开更多
This paper deals with higher-order optimality conditions for Henig effcient solutions of set-valued optimization problems.By virtue of the higher-order tangent sets, necessary and suffcient conditions are obtained for...This paper deals with higher-order optimality conditions for Henig effcient solutions of set-valued optimization problems.By virtue of the higher-order tangent sets, necessary and suffcient conditions are obtained for Henig effcient solutions of set-valued optimization problems whose constraint condition is determined by a fixed set.展开更多
This paper explores the conditions which make a regular balancedrandom(k,2s)-CNFformula(1,O)-unsatisfiable with high probability.The conditions also make a random instance of the regular balanced(k-1,2(k-1)s)-SAT prob...This paper explores the conditions which make a regular balancedrandom(k,2s)-CNFformula(1,O)-unsatisfiable with high probability.The conditions also make a random instance of the regular balanced(k-1,2(k-1)s)-SAT problem unsatisfiable with high probability,where the instance obeys a distribution which differs from the distribution obeyed by a regular balanced random(k-1,2(k-1)s)-CNF formula.Let F be a regular balanced random(k,2s)-CNF formula where k≥3,then there exists a number so such that F is(1,O)-unsatisfiable with high probability if s>so.A numerical solution of the number so when k e(5,6,...,14)is given to conduct simulated experiments.The simulated experiments verify the theoretical result.Besides,the experiments also suggest that F is(1,O)-satisfiable with high probability if s is less than a certain value.展开更多
This paper establishes some suffcient conditions for the lower semicontinuity of the effcient solution mapping for the semi-infinite vector optimization problem with perturbations of both the objective function and th...This paper establishes some suffcient conditions for the lower semicontinuity of the effcient solution mapping for the semi-infinite vector optimization problem with perturbations of both the objective function and the constraint set in normed linear spaces. The constraint set is the set of weakly effcient solutions of vector equilibrium problem, and perturbed by the perturbation of the criterion mapping to the vector equilibrium problem.展开更多
基金Supported by the Natural Science Foundation of the Education Department of Henan Province（2004110008）
文摘In this paper,the ε-super effcient solution for set-valued map vector optimization in locally convex space is introduced.And under the assumption of the nearly generalized cone-subconvexlikeness for set-valued maps,used new methods,the scalarization theorem and Lagrange multiplier theorem for ε-super effcient solution are established.
基金Supported by the National Natural Science Foundation of China（10871216） Supported by the Science and Technology Research Project of Chongqing Municipal Education Commission（KJ100419） Supported by the Natural Science Foundation Project of CQ CSTC（cstcjjA00019）
文摘This paper deals with higher-order optimality conditions for Henig effcient solutions of set-valued optimization problems.By virtue of the higher-order tangent sets, necessary and suffcient conditions are obtained for Henig effcient solutions of set-valued optimization problems whose constraint condition is determined by a fixed set.
基金Scientific Research Project for Introduced Talents of Guizhou University of Finance and Economics(No.2021YJ007)National Natural Science Foundation of China(Grant Nos.61862051,61762019,62241206)+2 种基金Top-notch Talent Program of Guizhou Province(No.KY[2018]080)Science and Technology Foundation of Guizhou Province(No.20191299)foundation of Qiannan Normal University for Nationalities(Nos.QNSYRC201715,QNSY2018JS013).
文摘This paper explores the conditions which make a regular balancedrandom(k,2s)-CNFformula(1,O)-unsatisfiable with high probability.The conditions also make a random instance of the regular balanced(k-1,2(k-1)s)-SAT problem unsatisfiable with high probability,where the instance obeys a distribution which differs from the distribution obeyed by a regular balanced random(k-1,2(k-1)s)-CNF formula.Let F be a regular balanced random(k,2s)-CNF formula where k≥3,then there exists a number so such that F is(1,O)-unsatisfiable with high probability if s>so.A numerical solution of the number so when k e(5,6,...,14)is given to conduct simulated experiments.The simulated experiments verify the theoretical result.Besides,the experiments also suggest that F is(1,O)-satisfiable with high probability if s is less than a certain value.
基金supported by the National Natural Science Foundation of China under Grant Nos.1106102311201216and 11471291
文摘This paper establishes some suffcient conditions for the lower semicontinuity of the effcient solution mapping for the semi-infinite vector optimization problem with perturbations of both the objective function and the constraint set in normed linear spaces. The constraint set is the set of weakly effcient solutions of vector equilibrium problem, and perturbed by the perturbation of the criterion mapping to the vector equilibrium problem.
