In this paper, we combine the nonmonotone and adaptive techniques with trust region method for unconstrained minimization problems. We set a new ratio of the actual descent and predicted descent. Then, instead of the ...In this paper, we combine the nonmonotone and adaptive techniques with trust region method for unconstrained minimization problems. We set a new ratio of the actual descent and predicted descent. Then, instead of the monotone sequence, the nonmonotone sequence of function values are employed. With the adaptive technique, the radius of trust region △k can be adjusted automatically to improve the efficiency of trust region methods. By means of the Bunch-Parlett factorization, we construct a method with indefinite dogleg path for solving the trust region subproblem which can handle the indefinite approximate Hessian Bk. The convergence properties of the algorithm are established. Finally, detailed numerical results are reported to show that our algorithm is efficient.展开更多
In this paper, we establish a theoretical framework of path-following interior point al- gorithms for the linear complementarity problems over symmetric cones (SCLCP) with the Cartesian P*(κ)-property, a weaker condi...In this paper, we establish a theoretical framework of path-following interior point al- gorithms for the linear complementarity problems over symmetric cones (SCLCP) with the Cartesian P*(κ)-property, a weaker condition than the monotonicity. Based on the Nesterov-Todd, xy and yx directions employed as commutative search directions for semidefinite programming, we extend the variants of the short-, semilong-, and long-step path-following algorithms for symmetric conic linear programming proposed by Schmieta and Alizadeh to the Cartesian P*(κ)-SCLCP, and particularly show the global convergence and the iteration complexities of the proposed algorithms.展开更多
Making use of the theory of continuous homotopy and the relation betweensymmetric polynomtal and polynomtal in one variable the arthors devoted ims article to constructing a regularly homotopic curve with probability ...Making use of the theory of continuous homotopy and the relation betweensymmetric polynomtal and polynomtal in one variable the arthors devoted ims article to constructing a regularly homotopic curve with probability one. Discrete tracingalong this honlotopic curve leads 10 a class of Durand-Kerner algorithm with stepparameters. The convergernce of this class of algorithms is given, which solves theconjecture about the global property of Durand-Kerner algorithm. The.problem forsteplength selection is thoroughly discussed Finally, sufficient numerical examples areused to verify our theory展开更多
This paper presents a new approach based on the particle swarm optimization (PSO) algorithm for solving the drilling path optimization problem belonging to discrete space.Because the standard PSO algorithm is not guar...This paper presents a new approach based on the particle swarm optimization (PSO) algorithm for solving the drilling path optimization problem belonging to discrete space.Because the standard PSO algorithm is not guaranteed to be global convergence or local convergence,based on the mathematical algorithm model,the algorithm is improved by adopting the method of generate the stop evolution particle over again to get the ability of convergence to the global optimization solution.And the operators are improved by establishing the duality transposition method and the handle manner for the elements of the operator,the improved operator can satisfy the need of integer coding in drilling path optimization.The experiment with small node numbers indicates that the improved algorithm has the characteristics of easy realize,fast convergence speed,and better global convergence characteris- tics.hence the new PSO can play a role in solving the problem of drilling path optimization in drilling holes.展开更多
基金Supported by the NNSF(10231060 and 10501024)of Chinathe Specialized Research Fund(20040319003)of Doctoral Program of Higher Education of China+1 种基金the Natural Science Grant(BK2006214)of Jiangsu Province of Chinathe Foundation(2004NXY20)of Nanjing Xiaozhuang College.
文摘In this paper, we combine the nonmonotone and adaptive techniques with trust region method for unconstrained minimization problems. We set a new ratio of the actual descent and predicted descent. Then, instead of the monotone sequence, the nonmonotone sequence of function values are employed. With the adaptive technique, the radius of trust region △k can be adjusted automatically to improve the efficiency of trust region methods. By means of the Bunch-Parlett factorization, we construct a method with indefinite dogleg path for solving the trust region subproblem which can handle the indefinite approximate Hessian Bk. The convergence properties of the algorithm are established. Finally, detailed numerical results are reported to show that our algorithm is efficient.
基金supported by National Natural Science Foundation of China (Grant Nos. 10671010, 70841008)
文摘In this paper, we establish a theoretical framework of path-following interior point al- gorithms for the linear complementarity problems over symmetric cones (SCLCP) with the Cartesian P*(κ)-property, a weaker condition than the monotonicity. Based on the Nesterov-Todd, xy and yx directions employed as commutative search directions for semidefinite programming, we extend the variants of the short-, semilong-, and long-step path-following algorithms for symmetric conic linear programming proposed by Schmieta and Alizadeh to the Cartesian P*(κ)-SCLCP, and particularly show the global convergence and the iteration complexities of the proposed algorithms.
文摘Making use of the theory of continuous homotopy and the relation betweensymmetric polynomtal and polynomtal in one variable the arthors devoted ims article to constructing a regularly homotopic curve with probability one. Discrete tracingalong this honlotopic curve leads 10 a class of Durand-Kerner algorithm with stepparameters. The convergernce of this class of algorithms is given, which solves theconjecture about the global property of Durand-Kerner algorithm. The.problem forsteplength selection is thoroughly discussed Finally, sufficient numerical examples areused to verify our theory
基金Supported by science and technology development fund of Fuzhou university(2005-XQ-09).
文摘This paper presents a new approach based on the particle swarm optimization (PSO) algorithm for solving the drilling path optimization problem belonging to discrete space.Because the standard PSO algorithm is not guaranteed to be global convergence or local convergence,based on the mathematical algorithm model,the algorithm is improved by adopting the method of generate the stop evolution particle over again to get the ability of convergence to the global optimization solution.And the operators are improved by establishing the duality transposition method and the handle manner for the elements of the operator,the improved operator can satisfy the need of integer coding in drilling path optimization.The experiment with small node numbers indicates that the improved algorithm has the characteristics of easy realize,fast convergence speed,and better global convergence characteris- tics.hence the new PSO can play a role in solving the problem of drilling path optimization in drilling holes.
