The Nesterov accelerated dynamical approach serves as an essential tool for addressing convex optimization problems with accelerated convergence rates.Most previous studies in this field have primarily concentrated on...The Nesterov accelerated dynamical approach serves as an essential tool for addressing convex optimization problems with accelerated convergence rates.Most previous studies in this field have primarily concentrated on unconstrained smooth con-vex optimization problems.In this paper,on the basis of primal-dual dynamical approach,Nesterov accelerated dynamical approach,projection operator and directional gradient,we present two accelerated primal-dual projection neurodynamic approaches with time scaling to address convex optimization problems with smooth and nonsmooth objective functions subject to linear and set constraints,which consist of a second-order ODE(ordinary differential equation)or differential conclusion system for the primal variables and a first-order ODE for the dual vari-ables.By satisfying specific conditions for time scaling,we demonstrate that the proposed approaches have a faster conver-gence rate.This only requires assuming convexity of the objective function.We validate the effectiveness of our proposed two accel-erated primal-dual projection neurodynamic approaches through numerical experiments.展开更多
With the help of the Maple symbolic computation system and the projective equation approach,a new family of variable separation solutions with arbitrary functions for the(2+1)-dimensional generalized Breor-Kaup(GB...With the help of the Maple symbolic computation system and the projective equation approach,a new family of variable separation solutions with arbitrary functions for the(2+1)-dimensional generalized Breor-Kaup(GBK) system is derived.Based on the derived solitary wave solution,some chaotic behaviors of the GBK system are investigated.展开更多
By an improved projective equation approach and a linear variable separation approach, a new family of exact solutions of the (2+1)-dimensional Broek-Kaup system is derived. Based on the derived solitary wave solut...By an improved projective equation approach and a linear variable separation approach, a new family of exact solutions of the (2+1)-dimensional Broek-Kaup system is derived. Based on the derived solitary wave solution and by selecting appropriate functions, some novel localized excitations such as instantaneous solitons and fractal solitons are investigated.展开更多
The paper studies on case-based reasoning of uncertain product attributes in configuration design of a product family. Interval numbers characterize uncertain product attributes. By interpolating a number of certain v...The paper studies on case-based reasoning of uncertain product attributes in configuration design of a product family. Interval numbers characterize uncertain product attributes. By interpolating a number of certain values randomly to replace interval numbers and making projection pursuit analysis on source cases and target cases of expanded numbers, we can get a projection value in the optimal projection direction. Based on projection value, we can construct a case retrieval model of projection pursuit that can handle coexisting certain and uncertain product attributes. The application examples of chainsaw configuration design show that case retrieval is highly sensitive to reliable results.展开更多
基金supported by the National Natural Science Foundation of China(62176218,62176027)the Fundamental Research Funds for the Central Universities(XDJK2020TY003)the Funds for Chongqing Talent Plan(cstc2024ycjh-bgzxm0082)。
文摘The Nesterov accelerated dynamical approach serves as an essential tool for addressing convex optimization problems with accelerated convergence rates.Most previous studies in this field have primarily concentrated on unconstrained smooth con-vex optimization problems.In this paper,on the basis of primal-dual dynamical approach,Nesterov accelerated dynamical approach,projection operator and directional gradient,we present two accelerated primal-dual projection neurodynamic approaches with time scaling to address convex optimization problems with smooth and nonsmooth objective functions subject to linear and set constraints,which consist of a second-order ODE(ordinary differential equation)or differential conclusion system for the primal variables and a first-order ODE for the dual vari-ables.By satisfying specific conditions for time scaling,we demonstrate that the proposed approaches have a faster conver-gence rate.This only requires assuming convexity of the objective function.We validate the effectiveness of our proposed two accel-erated primal-dual projection neurodynamic approaches through numerical experiments.
基金Project supported by the Natural Science Foundation of Zhejiang Province,China (Grant Nos. Y6100257,Y6090545,and Y6110140)the Scientific Research Fund of Zhejiang Provincial Education Department,China (Grant No. Z201120169)
文摘With the help of the Maple symbolic computation system and the projective equation approach,a new family of variable separation solutions with arbitrary functions for the(2+1)-dimensional generalized Breor-Kaup(GBK) system is derived.Based on the derived solitary wave solution,some chaotic behaviors of the GBK system are investigated.
基金Project supported by the Natural Science Foundation of Zhejiang Province of China (Grant Nos. Y606252 and Y604106)the Scientific Research Fund of the Education Department of Zhejiang Province of China (Grant No. 200805981)the Natural Science Foundation of Zhejiang Lishui University (Grant No. KZ09005)
文摘By an improved projective equation approach and a linear variable separation approach, a new family of exact solutions of the (2+1)-dimensional Broek-Kaup system is derived. Based on the derived solitary wave solution and by selecting appropriate functions, some novel localized excitations such as instantaneous solitons and fractal solitons are investigated.
文摘The paper studies on case-based reasoning of uncertain product attributes in configuration design of a product family. Interval numbers characterize uncertain product attributes. By interpolating a number of certain values randomly to replace interval numbers and making projection pursuit analysis on source cases and target cases of expanded numbers, we can get a projection value in the optimal projection direction. Based on projection value, we can construct a case retrieval model of projection pursuit that can handle coexisting certain and uncertain product attributes. The application examples of chainsaw configuration design show that case retrieval is highly sensitive to reliable results.