《《an interior affine scaling》.pdf

Journal of Computational and Applied Mathematics 173 (2005) 115–148 ./locate/cam An interior ane scaling projective algorithm for nonlinear equality and linear inequality constrained optimization Detong Zhu Department of Mathematics, Shanghai Normal University, Shanghai 200234, China Received 15 July 2003; received in revised form 25 January 2004 Abstract In this paper, we propose a ne wnonmonotonic interior point backtracking strategy to modify the reduced projective ane scaling trust region algorithm for solving optimization subject to nonlinear equality and linear inequality constraints. The general full trust region subproblem for solving the nonlinear equality and linear inequality constrained optimization is decomposed to a pair of trust region subproblems in horizontal and vertical subspaces of linearize equality constraints and extended ane scaling equality constraints. The horizontal subproblem in the proposed algorithm is dened by minimizing a quadratic projective reduced Hessian function subject only to an ellipsoidal trust region constraint in a null subspace of the tangential space, while the vertical subproblem is also dened by the least squares subproblem subject only to an ellipsoidal trust region constraint. By introducing the Fletcher’s penalty function as the merit function, trust region strategy with interior point backtracking technique will switch to strictly feasible interior point step generated by a component direction of the two