This paper presents the generalized reduced gradient method （GRG） and its realization forms. The application example of GRG in the optimization design of a single-stage cylindrical gear reducer is introduced. The al...This paper presents the generalized reduced gradient method （GRG） and its realization forms. The application example of GRG in the optimization design of a single-stage cylindrical gear reducer is introduced. The algo- rithm of the GRG method is realized in Vissim software. Based on the mathematical model of the single-stage cylin- drical gear reducer, the simulation structure of the optimization design was achieved. The experiment results show that the GRG method has fewer iterations and higher precision. The GRG method is very suitable for solving mechanical optimization design.展开更多
Based on the numerical governing formulation and non-linear complementary conditions of contact and impact problems, a reduced projection augmented Lagrange bi- conjugate gradient method is proposed for contact and im...Based on the numerical governing formulation and non-linear complementary conditions of contact and impact problems, a reduced projection augmented Lagrange bi- conjugate gradient method is proposed for contact and impact problems by translating non-linear complementary conditions into equivalent formulation of non-linear program- ming. For contact-impact problems, a larger time-step can be adopted arriving at numer- ical convergence compared with penalty method. By establishment of the impact-contact formulations which are equivalent with original non-linear complementary conditions, a reduced projection augmented Lagrange bi-conjugate gradient method is deduced to im- prove precision and efficiency of numerical solutions. A numerical example shows that the algorithm we suggested is valid and exact.展开更多
As the proportion of natural gas consumption in the energy market gradually increases,optimizing the design of gas storage surface system(GSSS)has become a current research focus.Existing studies on the two independen...As the proportion of natural gas consumption in the energy market gradually increases,optimizing the design of gas storage surface system(GSSS)has become a current research focus.Existing studies on the two independent injection pipeline network(InNET)and production pipeline network(ProNET)for underground natural gas storage(UNGS)are scarce,and no optimization methods have been proposed yet.Therefore,this paper focuses on the flow and pressure boundary characteristics of the GSSS.It constructs systematic models,including the injection multi-condition coupled model(INM model),production multi-condition coupled model(PRM model),injection single condition model(INS model)and production single condition model(PRS model)to optimize the design parameters.Additionally,this paper proposes a hybrid genetic algorithm based on generalized reduced gradient(HGA-GRG)for solving the models.The models and algorithm are applied to a case study with the objective of minimizing the cost of the pipeline network.For the GSSS,nine different condition scenarios are considered,and iterative process analysis and sensitivity analysis of these scenarios are conducted.Moreover,simulation scenarios are set up to verify the applicability of different scenarios to the boundaries.The research results show that the cost of the InNET considering the coupled pressure boundary is 64.4890×10^(4) CNY,and the cost of the ProNET considering coupled flow and pressure boundaries is 87.7655×10^(4) CNY,demonstrating greater applicability and economy than those considering only one or two types of conditions.The algorithms and models proposed in this paper provide an effective means for the design of parameters for GSSS.展开更多
In this paper we discuss the degeneracy in nonlinear programming with linear constraints, and give a technique for dealing with degeneracy in a general model of reduced gradient algorithms. Under the assumption that t...In this paper we discuss the degeneracy in nonlinear programming with linear constraints, and give a technique for dealing with degeneracy in a general model of reduced gradient algorithms. Under the assumption that the objective function is continuously differentiable, we prove that either the iterative sequence {xk} generated by the method terminates at a Kuhn-Tucker point after a finite number of iterations, or any cluster point of the sequence {xk} is a KuhnTucker point.展开更多
In this paper,we propose an accelerated stochastic variance reduction gradient method with a trust-region-like framework,referred as the NMSVRG-TR method.Based on NMSVRG,we incorporate a Katyusha-like acceleration ste...In this paper,we propose an accelerated stochastic variance reduction gradient method with a trust-region-like framework,referred as the NMSVRG-TR method.Based on NMSVRG,we incorporate a Katyusha-like acceleration step into the stochastic trust region scheme,which improves the convergence rate of the SVRG methods.Under appropriate assumptions,the linear convergence of the algorithm is provided for strongly convex objective functions.Numerical experiment results show that our algorithm is generally superior to some existing stochastic gradient methods.展开更多
A nitrogen-containing ionic liquid was synthesized using an aromatic nitrogen-containing heterocyclic and an amino acid,and applied to the extractive desulfurization process to remove benzothiophene,dibenzothiophene,a...A nitrogen-containing ionic liquid was synthesized using an aromatic nitrogen-containing heterocyclic and an amino acid,and applied to the extractive desulfurization process to remove benzothiophene,dibenzothiophene,and 4,6-dimethyldibenzothiphene from a model fuel oil.Chemical characterizations and simulation using Gaussian 09 software confirmed the rationality of an ionic liquid structure.Classification of non-covalent interactions between the ionic liquid and the three sulfur-containing contaminants was studied by reduced density gradient analysis.The viscosity of the ionic liquid was adjusted by addition of polyethylene glycol.Under extraction conditions of the volume of ionic liquid to oil as 1:1 and temperature as room temperature,the desulfurization selectivity of ionic liquid followed the order of 4,6-dimethyldibenzothiphene(15 min)<benzothiophene(15 min)≈dibenzothiophene(10 min).Addition of p-xylene and cyclohexene to the fuel oil had little effect.The extractant remained stable and effective after multiple regeneration cycles.展开更多
文摘This paper presents the generalized reduced gradient method （GRG） and its realization forms. The application example of GRG in the optimization design of a single-stage cylindrical gear reducer is introduced. The algo- rithm of the GRG method is realized in Vissim software. Based on the mathematical model of the single-stage cylin- drical gear reducer, the simulation structure of the optimization design was achieved. The experiment results show that the GRG method has fewer iterations and higher precision. The GRG method is very suitable for solving mechanical optimization design.
文摘Based on the numerical governing formulation and non-linear complementary conditions of contact and impact problems, a reduced projection augmented Lagrange bi- conjugate gradient method is proposed for contact and impact problems by translating non-linear complementary conditions into equivalent formulation of non-linear program- ming. For contact-impact problems, a larger time-step can be adopted arriving at numer- ical convergence compared with penalty method. By establishment of the impact-contact formulations which are equivalent with original non-linear complementary conditions, a reduced projection augmented Lagrange bi-conjugate gradient method is deduced to im- prove precision and efficiency of numerical solutions. A numerical example shows that the algorithm we suggested is valid and exact.
基金funded by the National Natural Science Foun-dation of China,grant number 51704253 and 52474084。
文摘As the proportion of natural gas consumption in the energy market gradually increases,optimizing the design of gas storage surface system(GSSS)has become a current research focus.Existing studies on the two independent injection pipeline network(InNET)and production pipeline network(ProNET)for underground natural gas storage(UNGS)are scarce,and no optimization methods have been proposed yet.Therefore,this paper focuses on the flow and pressure boundary characteristics of the GSSS.It constructs systematic models,including the injection multi-condition coupled model(INM model),production multi-condition coupled model(PRM model),injection single condition model(INS model)and production single condition model(PRS model)to optimize the design parameters.Additionally,this paper proposes a hybrid genetic algorithm based on generalized reduced gradient(HGA-GRG)for solving the models.The models and algorithm are applied to a case study with the objective of minimizing the cost of the pipeline network.For the GSSS,nine different condition scenarios are considered,and iterative process analysis and sensitivity analysis of these scenarios are conducted.Moreover,simulation scenarios are set up to verify the applicability of different scenarios to the boundaries.The research results show that the cost of the InNET considering the coupled pressure boundary is 64.4890×10^(4) CNY,and the cost of the ProNET considering coupled flow and pressure boundaries is 87.7655×10^(4) CNY,demonstrating greater applicability and economy than those considering only one or two types of conditions.The algorithms and models proposed in this paper provide an effective means for the design of parameters for GSSS.
文摘In this paper we discuss the degeneracy in nonlinear programming with linear constraints, and give a technique for dealing with degeneracy in a general model of reduced gradient algorithms. Under the assumption that the objective function is continuously differentiable, we prove that either the iterative sequence {xk} generated by the method terminates at a Kuhn-Tucker point after a finite number of iterations, or any cluster point of the sequence {xk} is a KuhnTucker point.
文摘In this paper,we propose an accelerated stochastic variance reduction gradient method with a trust-region-like framework,referred as the NMSVRG-TR method.Based on NMSVRG,we incorporate a Katyusha-like acceleration step into the stochastic trust region scheme,which improves the convergence rate of the SVRG methods.Under appropriate assumptions,the linear convergence of the algorithm is provided for strongly convex objective functions.Numerical experiment results show that our algorithm is generally superior to some existing stochastic gradient methods.
基金This work was supported by the National Natural Science Foundation of China(Grant Nos.22125802,22078010 and U1862113)the Big Science Project from BUCT(Grant No.XK180301).
文摘A nitrogen-containing ionic liquid was synthesized using an aromatic nitrogen-containing heterocyclic and an amino acid,and applied to the extractive desulfurization process to remove benzothiophene,dibenzothiophene,and 4,6-dimethyldibenzothiphene from a model fuel oil.Chemical characterizations and simulation using Gaussian 09 software confirmed the rationality of an ionic liquid structure.Classification of non-covalent interactions between the ionic liquid and the three sulfur-containing contaminants was studied by reduced density gradient analysis.The viscosity of the ionic liquid was adjusted by addition of polyethylene glycol.Under extraction conditions of the volume of ionic liquid to oil as 1:1 and temperature as room temperature,the desulfurization selectivity of ionic liquid followed the order of 4,6-dimethyldibenzothiphene(15 min)<benzothiophene(15 min)≈dibenzothiophene(10 min).Addition of p-xylene and cyclohexene to the fuel oil had little effect.The extractant remained stable and effective after multiple regeneration cycles.
