An Interior Trust Region Algorithm For Nonlinear Minimization With Linear Constraints
Jian Guo Liu 11 Department of Mathematics, University of North Texas, Denton, TX 76203, USA
An interior trust-region-based algorithm for linearly constained minimization problems is proposed and analyzed. This algorithm is similar to trust region algorithms for unconstrained minimization: a trust region subproblem on a subspace is solved in each iteration.We establish that the proposed algorithm has convergence properties analogous point of the generated sequence satisfies the Krush-Kuhn-Tucker (KKT)conditions and at least one limit point satisfies second order necessary optimatity conditions. In addition, if one limit point is a strong local minimizer and the Hessian is Lipschitz continuous in a neighborbood of that point, then the generated sequence converges globally to that point in the rate of at least 2-step quadratic. We are mainly concerned with the theoretical properties of the algorithm in this paper. Implementation issues and adaptation to large-scale problems will be addressed in a future report.
Key words: Nonlinear programming; Linear constraints; Trust region algorithms; Newton methods.