In classical nonlinear programming, it is a general method of developing optimality conditions that a nonlinear programming problem is linearized as a linear programming problem by using first order approximations of ...In classical nonlinear programming, it is a general method of developing optimality conditions that a nonlinear programming problem is linearized as a linear programming problem by using first order approximations of the functions at a given feasible point. The linearized procedure for differentiable nonlinear programming problems can be naturally generalized to the quasi differential case. As in classical case so called constraint qualifications have to be imposed on the constraint functions to guarantee that for a given local minimizer of the original problem the nullvector is an optimal solution of the corresponding 'quasilinearized' problem. In this paper, constraint qualifications for inequality constrained quasi differentiable programming problems of type min {f(x)|g(x)≤0} are considered, where f and g are qusidifferentiable functions in the sense of Demyanov. Various constraint qualifications for this problem are presented and a new one is proposed. The relations among these conditions are investigated. Moreover, a Wolf dual problem for this problem is introduced, and the corresponding dual theorems are given.展开更多
In this paper,C1,1 regularity for solutions to the degenerate dual Orlicz-Minkowski problem is considered.The dual Orlicz-Minkowski problem is a generalization of the Lp dual Minkowski problem in convex geometry.The p...In this paper,C1,1 regularity for solutions to the degenerate dual Orlicz-Minkowski problem is considered.The dual Orlicz-Minkowski problem is a generalization of the Lp dual Minkowski problem in convex geometry.The proof is adapted from Guan-Li[17]and Chen-Tu-Wu-Xiang[11].展开更多
This paper gives a new dual problem for nondifferentiable convex programming and provesthe properties of weak duality and strong duality and offers a necessary and sufficient condition ofstrong duality.
In this paper, a class of nonsmooth multiobjective programming problems is considered. We introduce the new concept of invex of order??type II for nondifferentiable locally Lipschitz functions using the tools of Clark...In this paper, a class of nonsmooth multiobjective programming problems is considered. We introduce the new concept of invex of order??type II for nondifferentiable locally Lipschitz functions using the tools of Clarke subdifferential. The new functions are used to derive the sufficient optimality condition for a class of nonsmooth multiobjective programming problems. Utilizing the sufficient optimality conditions, weak and strong duality theorems are established for Wolfe type duality model.展开更多
A series of problems in mechanics and physics are governed by the ordinary Poisson equation which demands linearity,isotropy,and material homo- geneity.In this paper a generalization with respect to nonlinearity,aniso...A series of problems in mechanics and physics are governed by the ordinary Poisson equation which demands linearity,isotropy,and material homo- geneity.In this paper a generalization with respect to nonlinearity,anisotropy,and inhomogeneity is made.Starting from the canonical basic equations in the primal and dual formulation respectively we derive systematically the corresponding generalized variational principles;under certain conditions they can be extended to so called complementary extremum principles allowing for global bounds.For simplicity a restriction to two dimensional problems is made,including twice-connected domains.展开更多
In this paper,we consider nonlinear infinity-norm minimization problems.We device a reliable Lagrangian dual approach for solving this kind of problems and based on this method we propose an algorithm for the mixed li...In this paper,we consider nonlinear infinity-norm minimization problems.We device a reliable Lagrangian dual approach for solving this kind of problems and based on this method we propose an algorithm for the mixed linear and nonlinear infinity- norm minimization problems.Numerical results are presented.展开更多
Multi-dimensional nonlinear knapsack problems are often encountered in resource allocation, industrial planning and computer networks. In this paper, a surrogate dual method was proposed for solving this class of prob...Multi-dimensional nonlinear knapsack problems are often encountered in resource allocation, industrial planning and computer networks. In this paper, a surrogate dual method was proposed for solving this class of problems. Multiply constrained problem was relaxed to a singly constrained problem by using the surrogate technique. To compute tighter bounds of the primal problem, the cutting plane method was used to solve the surrogate dual problem, where the surrogate relaxation problem was solved by the 0-1 linearization method. The domain cut technique was employed to eliminate the duality gap and thus to guarantee the convergence of tile algorithm. Numerical results were reported for large-scale multi-dimensional nonlinear knapsack problems.展开更多
随着电子商务的爆发式发展,城市末端配送面临需求波动与服务时间不确定性的双重挑战,传统单模式配送(仅支持上门直送或仅支持快递柜自取)难以兼顾成本效率与服务可靠性。针对这一问题,文中提出融合智能快递柜的双模式车辆路径问题(dual-...随着电子商务的爆发式发展,城市末端配送面临需求波动与服务时间不确定性的双重挑战,传统单模式配送(仅支持上门直送或仅支持快递柜自取)难以兼顾成本效率与服务可靠性。针对这一问题,文中提出融合智能快递柜的双模式车辆路径问题(dual-mode vehicle routing problem with parcel lockers,DM-VRP-PL),构建了综合固定成本、运输成本与时间窗惩罚成本的混合整数规划模型,并设计随机优化遗传算法(ROGA)进行高效求解。该算法创新性地采用“趋优-随机”混合交叉策略,结合累积排序适应度分配机制,有效平衡了收敛速度与种群多样性。基于标准VRP测试实例的实验表明,双模式配送系统在成本控制与配送效率方面显著优于单模式方案。进一步分析揭示了快递柜覆盖半径对系统性能的非线性影响规律。研究为不同发展阶段的城市末端物流网络提供了分层优化的决策框架与量化工具,对智能快递柜的科学布局与双模式配送系统的实际部署具有重要参考价值。展开更多
Recently, the notion of general （containing symmetric and asymmetric） Lp-intersection bodies was given. In this article, by the Lp-dual mixed volumes and the general Lp-dual Blaschke bodies, we study the Lp-dual aff...Recently, the notion of general （containing symmetric and asymmetric） Lp-intersection bodies was given. In this article, by the Lp-dual mixed volumes and the general Lp-dual Blaschke bodies, we study the Lp-dual affine surface area forms of the Busemann-Petty problems for general Lp-intersection bodies. Our works belong to a new and rapidly evolving asymmetric Lp-Brtmn-Minkowski theory.展开更多
With the rapid development of the individualized demand market,the demand for manufacturing flexibility has increased over time.As a result,a cell manufacturing system suitable for many varieties and small batches has...With the rapid development of the individualized demand market,the demand for manufacturing flexibility has increased over time.As a result,a cell manufacturing system suitable for many varieties and small batches has been produced.With the goal of minimizing the area and logistics handling volume,and considering the arrangement order of facilities and channel constraints,a mathematical model was established,and the problem was solved by improved NSGA-II.After non-dominated sorting,traditional NSGA-II will cross-operate the individuals with the best sorting to generate new individuals.Such a selection strategy is extremely easy to fall into the local optimal solution.The improved NSGA-II is to improve the original selection operation,which is to select the first half of the excellent individuals in the non-dominated sorting into the cross operation,and then select the last sorted ones of the remaining individuals into the cross operation,and combine the best and the worst ones into the cross operation.Finally,an example is given to simulate and improve the solution of NSGA-II and NSGA-II.The simulation results indicate that the improved NSGA-II population shows more obvious diversity,it is easier to jump out of the local optimal solution than NSGA-II,and the satisfactory layout scheme of manufacturing cells is obtained.Therefore,it is more effective to use improved NSGA-II to solve the problem of manufacturing cell layout.展开更多
develop a mentation This paper considers the priority facility primal-dual 3-approximation algorithm for procedure, the authors further improve the location problem with penalties： The authors this problem. Combining...develop a mentation This paper considers the priority facility primal-dual 3-approximation algorithm for procedure, the authors further improve the location problem with penalties： The authors this problem. Combining with the greedy aug- previous ratio 3 to 1.8526.展开更多
this paper,we establish the a priori estimates for solutions of mixed Hessian quotient type equations on S^(n).Then we obtain the existence and uniqueness of Γ_(k)-admissible solutions to the Lp dual Minkowski type p...this paper,we establish the a priori estimates for solutions of mixed Hessian quotient type equations on S^(n).Then we obtain the existence and uniqueness of Γ_(k)-admissible solutions to the Lp dual Minkowski type problem with p≥q.Moreover,we show the existence of convex solutions by Constant Rank Theorem.展开更多
In this article, we propose efficient methods for solving two stage transshipment problems. Transshipment problem is the special case of Minimum cost flow problem in which arc capacities are infinite. We start by prop...In this article, we propose efficient methods for solving two stage transshipment problems. Transshipment problem is the special case of Minimum cost flow problem in which arc capacities are infinite. We start by proposing a novel problem formulation for a two stage transshipment problem. Later, special structure of our problem formulation is utilized to devise two dual based heuristics solutions with computational complexity of O (n2), and O (n3) respectively. These methods are motivated by the methods developed by Sharma and Saxena [1], Sinha and Sharma [2]. Our methods differ in the initialization and the subsequent variation of the dual variables associated with the transshipment nodes along the shortest path. Lastly, a method is proposed to extract a very good primal solution from the given dual solutions with a computational complexity of O (n2). Efficacy of these methods is demonstrated by our numerical analysis on 200 random problems.展开更多
The stochastic dual dynamic programming (SDDP) algorithm is becoming increasingly used. In this paper we present analysis of different methods of lattice construction for SDDP exemplifying a realistic variant of the n...The stochastic dual dynamic programming (SDDP) algorithm is becoming increasingly used. In this paper we present analysis of different methods of lattice construction for SDDP exemplifying a realistic variant of the newsvendor problem, incorporating storage of production. We model several days of work and compare the profits realized using different methods of the lattice construction and the corresponding computer time spent in lattice construction. Our case differs from the known one because we consider not only a multidimensional but also a multistage case with stage dependence. We construct scenario lattice for different Markov processes which play a crucial role in stochastic modeling. The novelty of our work is comparing different methods of scenario lattice construction. We considered a realistic variant of the newsvendor problem. The results presented in this article show that the Voronoi method slightly outperforms others, but the k-means method is much faster overall.展开更多
文摘In classical nonlinear programming, it is a general method of developing optimality conditions that a nonlinear programming problem is linearized as a linear programming problem by using first order approximations of the functions at a given feasible point. The linearized procedure for differentiable nonlinear programming problems can be naturally generalized to the quasi differential case. As in classical case so called constraint qualifications have to be imposed on the constraint functions to guarantee that for a given local minimizer of the original problem the nullvector is an optimal solution of the corresponding 'quasilinearized' problem. In this paper, constraint qualifications for inequality constrained quasi differentiable programming problems of type min {f(x)|g(x)≤0} are considered, where f and g are qusidifferentiable functions in the sense of Demyanov. Various constraint qualifications for this problem are presented and a new one is proposed. The relations among these conditions are investigated. Moreover, a Wolf dual problem for this problem is introduced, and the corresponding dual theorems are given.
文摘In this paper,C1,1 regularity for solutions to the degenerate dual Orlicz-Minkowski problem is considered.The dual Orlicz-Minkowski problem is a generalization of the Lp dual Minkowski problem in convex geometry.The proof is adapted from Guan-Li[17]and Chen-Tu-Wu-Xiang[11].
文摘This paper gives a new dual problem for nondifferentiable convex programming and provesthe properties of weak duality and strong duality and offers a necessary and sufficient condition ofstrong duality.
文摘In this paper, a class of nonsmooth multiobjective programming problems is considered. We introduce the new concept of invex of order??type II for nondifferentiable locally Lipschitz functions using the tools of Clarke subdifferential. The new functions are used to derive the sufficient optimality condition for a class of nonsmooth multiobjective programming problems. Utilizing the sufficient optimality conditions, weak and strong duality theorems are established for Wolfe type duality model.
文摘A series of problems in mechanics and physics are governed by the ordinary Poisson equation which demands linearity,isotropy,and material homo- geneity.In this paper a generalization with respect to nonlinearity,anisotropy,and inhomogeneity is made.Starting from the canonical basic equations in the primal and dual formulation respectively we derive systematically the corresponding generalized variational principles;under certain conditions they can be extended to so called complementary extremum principles allowing for global bounds.For simplicity a restriction to two dimensional problems is made,including twice-connected domains.
文摘In this paper,we consider nonlinear infinity-norm minimization problems.We device a reliable Lagrangian dual approach for solving this kind of problems and based on this method we propose an algorithm for the mixed linear and nonlinear infinity- norm minimization problems.Numerical results are presented.
基金partially supported by the National Natural Science Foundation of China （Grant Nos.10271073, 10571116）
文摘Multi-dimensional nonlinear knapsack problems are often encountered in resource allocation, industrial planning and computer networks. In this paper, a surrogate dual method was proposed for solving this class of problems. Multiply constrained problem was relaxed to a singly constrained problem by using the surrogate technique. To compute tighter bounds of the primal problem, the cutting plane method was used to solve the surrogate dual problem, where the surrogate relaxation problem was solved by the 0-1 linearization method. The domain cut technique was employed to eliminate the duality gap and thus to guarantee the convergence of tile algorithm. Numerical results were reported for large-scale multi-dimensional nonlinear knapsack problems.
文摘随着电子商务的爆发式发展,城市末端配送面临需求波动与服务时间不确定性的双重挑战,传统单模式配送(仅支持上门直送或仅支持快递柜自取)难以兼顾成本效率与服务可靠性。针对这一问题,文中提出融合智能快递柜的双模式车辆路径问题(dual-mode vehicle routing problem with parcel lockers,DM-VRP-PL),构建了综合固定成本、运输成本与时间窗惩罚成本的混合整数规划模型,并设计随机优化遗传算法(ROGA)进行高效求解。该算法创新性地采用“趋优-随机”混合交叉策略,结合累积排序适应度分配机制,有效平衡了收敛速度与种群多样性。基于标准VRP测试实例的实验表明,双模式配送系统在成本控制与配送效率方面显著优于单模式方案。进一步分析揭示了快递柜覆盖半径对系统性能的非线性影响规律。研究为不同发展阶段的城市末端物流网络提供了分层优化的决策框架与量化工具,对智能快递柜的科学布局与双模式配送系统的实际部署具有重要参考价值。
基金Supported by the National Natural Science Foundation of China(11371224)
文摘Recently, the notion of general （containing symmetric and asymmetric） Lp-intersection bodies was given. In this article, by the Lp-dual mixed volumes and the general Lp-dual Blaschke bodies, we study the Lp-dual affine surface area forms of the Busemann-Petty problems for general Lp-intersection bodies. Our works belong to a new and rapidly evolving asymmetric Lp-Brtmn-Minkowski theory.
文摘With the rapid development of the individualized demand market,the demand for manufacturing flexibility has increased over time.As a result,a cell manufacturing system suitable for many varieties and small batches has been produced.With the goal of minimizing the area and logistics handling volume,and considering the arrangement order of facilities and channel constraints,a mathematical model was established,and the problem was solved by improved NSGA-II.After non-dominated sorting,traditional NSGA-II will cross-operate the individuals with the best sorting to generate new individuals.Such a selection strategy is extremely easy to fall into the local optimal solution.The improved NSGA-II is to improve the original selection operation,which is to select the first half of the excellent individuals in the non-dominated sorting into the cross operation,and then select the last sorted ones of the remaining individuals into the cross operation,and combine the best and the worst ones into the cross operation.Finally,an example is given to simulate and improve the solution of NSGA-II and NSGA-II.The simulation results indicate that the improved NSGA-II population shows more obvious diversity,it is easier to jump out of the local optimal solution than NSGA-II,and the satisfactory layout scheme of manufacturing cells is obtained.Therefore,it is more effective to use improved NSGA-II to solve the problem of manufacturing cell layout.
基金supported by the National Natural Science Foundation of China under Grant No.11371001
文摘develop a mentation This paper considers the priority facility primal-dual 3-approximation algorithm for procedure, the authors further improve the location problem with penalties： The authors this problem. Combining with the greedy aug- previous ratio 3 to 1.8526.
基金supported by the NSFC(11971157,12426532,12571213).
文摘this paper,we establish the a priori estimates for solutions of mixed Hessian quotient type equations on S^(n).Then we obtain the existence and uniqueness of Γ_(k)-admissible solutions to the Lp dual Minkowski type problem with p≥q.Moreover,we show the existence of convex solutions by Constant Rank Theorem.
文摘In this article, we propose efficient methods for solving two stage transshipment problems. Transshipment problem is the special case of Minimum cost flow problem in which arc capacities are infinite. We start by proposing a novel problem formulation for a two stage transshipment problem. Later, special structure of our problem formulation is utilized to devise two dual based heuristics solutions with computational complexity of O (n2), and O (n3) respectively. These methods are motivated by the methods developed by Sharma and Saxena [1], Sinha and Sharma [2]. Our methods differ in the initialization and the subsequent variation of the dual variables associated with the transshipment nodes along the shortest path. Lastly, a method is proposed to extract a very good primal solution from the given dual solutions with a computational complexity of O (n2). Efficacy of these methods is demonstrated by our numerical analysis on 200 random problems.
文摘The stochastic dual dynamic programming (SDDP) algorithm is becoming increasingly used. In this paper we present analysis of different methods of lattice construction for SDDP exemplifying a realistic variant of the newsvendor problem, incorporating storage of production. We model several days of work and compare the profits realized using different methods of the lattice construction and the corresponding computer time spent in lattice construction. Our case differs from the known one because we consider not only a multidimensional but also a multistage case with stage dependence. We construct scenario lattice for different Markov processes which play a crucial role in stochastic modeling. The novelty of our work is comparing different methods of scenario lattice construction. We considered a realistic variant of the newsvendor problem. The results presented in this article show that the Voronoi method slightly outperforms others, but the k-means method is much faster overall.
