Superlinearly Convergent Affine Scaling Interior Trust-Region Method for Linear Constrained LC^1 Minimization  

作　　者：De Tong ZHU 

机构地区：[1]Business College, Shanghai Normal University, Shanghai 200234, P. R. China

出　　处：《Acta Mathematica Sinica,English Series》2008年第12期2081-2100,共20页数学学报（英文版）

基　　金：the National Science Foundation Grant (10871130) of China;the Ph.D.Foundation Grant (0527003);the Shanghai Leading Academic Discipline Project (T0401);the Science Foundation Grant (05DZ11) of Shanghai Education Committee

摘　　要：We extend the classical affine scaling interior trust region algorithm for the linear constrained smooth minimization problem to the nonsmooth case where the gradient of objective function is only locally Lipschitzian. We propose and analyze a new affine scaling trust-region method in association with nonmonotonic interior backtracking line search technique for solving the linear constrained LC1 optimization where the second-order derivative of the objective function is explicitly required to be locally Lipschitzian. The general trust region subproblem in the proposed algorithm is defined by minimizing an augmented affine scaling quadratic model which requires both first and second order information of the objective function subject only to an affine scaling ellipsoidal constraint in a null subspace of the augmented equality constraints. The global convergence and fast local convergence rate of the proposed algorithm are established under some reasonable conditions where twice smoothness of the objective function is not required. Applications of the algorithm to some nonsmooth optimization problems are discussed.We extend the classical affine scaling interior trust region algorithm for the linear constrained smooth minimization problem to the nonsmooth case where the gradient of objective function is only locally Lipschitzian. We propose and analyze a new affine scaling trust-region method in association with nonmonotonic interior backtracking line search technique for solving the linear constrained LC1 optimization where the second-order derivative of the objective function is explicitly required to be locally Lipschitzian. The general trust region subproblem in the proposed algorithm is defined by minimizing an augmented affine scaling quadratic model which requires both first and second order information of the objective function subject only to an affine scaling ellipsoidal constraint in a null subspace of the augmented equality constraints. The global convergence and fast local convergence rate of the proposed algorithm are established under some reasonable conditions where twice smoothness of the objective function is not required. Applications of the algorithm to some nonsmooth optimization problems are discussed.

关 键 词：trust region method BACKTRACKING nonmonotonic technique interior point LC^1 minimization affine scaling 

分 类 号：O22[理学—运筹学与控制论]