Numerical Experiments on Dual Matrix Algorithms for Function Minimization

作     者：Huang, H. Y. Chambliss, J. P. 

作者机构：Rice Univ Dept Mech & Aerosp Engn & Mat Sci Houston TX 77251 USA 

出 版 物：《JOURNAL OF OPTIMIZATION THEORY AND APPLICATIONS》 (优选法理论与应用杂志)

年 卷 期：1974年第13卷第6期

页      面：620-634页

核心收录：

学科分类：1201[管理学-管理科学与工程(可授管理学、工学学位)] 07[理学] 070104[理学-应用数学] 0701[理学-数学] 

基　　金：National Science Foundation 

主　　题：Mathematical programming function minimization method of dual matrices computing methods numerical methods 

摘      要：In Ref. 2, four algorithms of dual matrices for function minimization were introduced. These algorithms are characterized by the simultaneous use of two matrices and by the property that the one-dimensional search for the optimal stepsize is not needed for convergence. For a quadratic function, these algorithms lead to the solution in at most n + 1 iterations, where n is the number of variables in the function. Since the one-dimensional search is not needed, the total number of gradient evaluations for convergence is at most n + 2. In this paper, the above-mentioned algorithms are tested numerically by using five nonquadratic functions. In order to investigate the effects of the stepsize on the performances of these algorithms, four schemes for the stepsize factor are employed, two corresponding to small-step processes and two corresponding to large-step processes. The numerical results show that, in spite of the wide range employed in the choice of the stepsize factor, all algorithms exhibit satisfactory convergence properties and compare favorably with the corresponding quadratically convergent algorithms using one-dimensional searches for optimal stepsizes.