Convergence analysis of a nonlinear Lagrange algorithm for general nonlinear constrained optimization problems  

作　　者：HE Su-xiang WU Li-xun 

机构地区：[1]School of Science, Wuhan University of Technology

出　　处：《Applied Mathematics(A Journal of Chinese Universities)》2014年第3期352-366,共15页高校应用数学学报（英文版）（B辑）

基　　金：Supported by the National Natural Science Foundation of China(11201357,81271513 and 91324201);the Fundamental Research Funds for the Central Universities under project(2014-Ia-001)

摘　　要：The convergence analysis of a nonlinear Lagrange algorithm for solving nonlinear constrained optimization problems with both inequality and equality constraints is explored in detail. The estimates for the derivatives of the multiplier mapping and the solution mapping of the proposed algorithm are discussed via the technique of the singular value decomposition of matrix. Based on the estimates, the local convergence results and the rate of convergence of the algorithm are presented when the penalty parameter is less than a threshold under a set of suitable conditions on problem functions. Furthermore, the condition number of the Hessian of the nonlinear Lagrange function with respect to the decision variables is analyzed, which is closely related to efficiency of the algorithm. Finally, the preliminary numericM results for several typical test problems are reported.The convergence analysis of a nonlinear Lagrange algorithm for solving nonlinear constrained optimization problems with both inequality and equality constraints is explored in detail. The estimates for the derivatives of the multiplier mapping and the solution mapping of the proposed algorithm are discussed via the technique of the singular value decomposition of matrix. Based on the estimates, the local convergence results and the rate of convergence of the algorithm are presented when the penalty parameter is less than a threshold under a set of suitable conditions on problem functions. Furthermore, the condition number of the Hessian of the nonlinear Lagrange function with respect to the decision variables is analyzed, which is closely related to efficiency of the algorithm. Finally, the preliminary numericM results for several typical test problems are reported.

关 键 词：nonlinear Lagrange algorithm general nonlinear constrained optimization problem solutionmapping multiplier mapping condition number. 

分 类 号：O224[理学—运筹学与控制论] O241.4[理学—数学]