A new algorithm based on genetic algorithm(GA) is developed for solving function optimization problems with inequality constraints. This algorithm has been used to a series of standard test problems and exhibited good...A new algorithm based on genetic algorithm(GA) is developed for solving function optimization problems with inequality constraints. This algorithm has been used to a series of standard test problems and exhibited good performance. The computation results show that its generality, precision, robustness, simplicity and performance are all satisfactory.展开更多
利用一些学者提出的一种研究全局最优化问题的全局最优性条件的新方法,讨论了一些带有二次约束的非凸二次规划问题的全局最优性条件。本文主要通过利用拉格朗日函数F(λ,u)=1/2xTH_(λ,u)x+b_(T,u)λx+sum from i=i∈I(λici)+sum from ...利用一些学者提出的一种研究全局最优化问题的全局最优性条件的新方法,讨论了一些带有二次约束的非凸二次规划问题的全局最优性条件。本文主要通过利用拉格朗日函数F(λ,u)=1/2xTH_(λ,u)x+b_(T,u)λx+sum from i=i∈I(λici)+sum from j=j∈Jμjcj,正则锥(NL,D(x0)={l∈L:l(y)-l(x0)≤0,y∈D})和L-次微分相结合的方法,给出了带不等式约束的混合整数二次规划最小问题的全局极小点的全局最优性充分条件,而且推广了现有文献中的一些结论。同时通过一些实值例子说明了本文给出的最优性充分条件的可行性和有效性。展开更多
Presents information on a study which proposed a superlinearly convergent algorithm of sequential systems of linear equations or nonlinear optimization problems with inequality constraints. Assumptions; Discussion on ...Presents information on a study which proposed a superlinearly convergent algorithm of sequential systems of linear equations or nonlinear optimization problems with inequality constraints. Assumptions; Discussion on lemmas about several matrices related to the common coefficient matrix F; Strengthening of the regularity assumptions on the functions involved; Numerical experiments.展开更多
Based on a new efficient identification technique of active constraints introduced in this paper, a new sequential systems of linear equations （SSLE） algorithm generating feasible iterates is proposed for solving no...Based on a new efficient identification technique of active constraints introduced in this paper, a new sequential systems of linear equations （SSLE） algorithm generating feasible iterates is proposed for solving nonlinear optimization problems with inequality constraints. In this paper, we introduce a new technique for constructing the system of linear equations, which recurs to a perturbation for the gradients of the constraint functions. At each iteration of the new algorithm, a feasible descent direction is obtained by solving only one system of linear equations without doing convex combination. To ensure the global convergence and avoid the Maratos effect, the algorithm needs to solve two additional reduced systems of linear equations with the same coefficient matrix after finite iterations. The proposed algorithm is proved to be globally and superlinearly convergent under some mild conditions. What distinguishes this algorithm from the previous feasible SSLE algorithms is that an improving direction is obtained easily and the computation cost of generating a new iterate is reduced. Finally, a preliminary implementation has been tested.展开更多
文摘A new algorithm based on genetic algorithm(GA) is developed for solving function optimization problems with inequality constraints. This algorithm has been used to a series of standard test problems and exhibited good performance. The computation results show that its generality, precision, robustness, simplicity and performance are all satisfactory.
文摘利用一些学者提出的一种研究全局最优化问题的全局最优性条件的新方法,讨论了一些带有二次约束的非凸二次规划问题的全局最优性条件。本文主要通过利用拉格朗日函数F(λ,u)=1/2xTH_(λ,u)x+b_(T,u)λx+sum from i=i∈I(λici)+sum from j=j∈Jμjcj,正则锥(NL,D(x0)={l∈L:l(y)-l(x0)≤0,y∈D})和L-次微分相结合的方法,给出了带不等式约束的混合整数二次规划最小问题的全局极小点的全局最优性充分条件,而且推广了现有文献中的一些结论。同时通过一些实值例子说明了本文给出的最优性充分条件的可行性和有效性。
基金This research was supported by the National Natural Science Foundation of China(19571001, 19971002, 79970014) Cross-century Excellent Personnel Award and Teaching and Research Award Program for Outstanding Young Teachers in High Education Ministry o
文摘Presents information on a study which proposed a superlinearly convergent algorithm of sequential systems of linear equations or nonlinear optimization problems with inequality constraints. Assumptions; Discussion on lemmas about several matrices related to the common coefficient matrix F; Strengthening of the regularity assumptions on the functions involved; Numerical experiments.
基金Supported by National Natural Science Foundation of China (Grant No. 10771040)Guangxi Science Foundation (Grant No. 0832052)Guangxi University for Nationalities Youth Foundation (Grant No. 2007QN24)
文摘Based on a new efficient identification technique of active constraints introduced in this paper, a new sequential systems of linear equations （SSLE） algorithm generating feasible iterates is proposed for solving nonlinear optimization problems with inequality constraints. In this paper, we introduce a new technique for constructing the system of linear equations, which recurs to a perturbation for the gradients of the constraint functions. At each iteration of the new algorithm, a feasible descent direction is obtained by solving only one system of linear equations without doing convex combination. To ensure the global convergence and avoid the Maratos effect, the algorithm needs to solve two additional reduced systems of linear equations with the same coefficient matrix after finite iterations. The proposed algorithm is proved to be globally and superlinearly convergent under some mild conditions. What distinguishes this algorithm from the previous feasible SSLE algorithms is that an improving direction is obtained easily and the computation cost of generating a new iterate is reduced. Finally, a preliminary implementation has been tested.
