Constructing Appropriate Models for Large-Scale, Linearly-Constrained, Nonconvex,Nonlinear Optimization Algorithms

摘要

The authors consider the algebraic issues concerning the solution of general,large-scale, linearly constrained nonlinear optimization problems. Particular attention is given to suitable methods for solving the linear systems which occur at each iteration of such methods. The main issue addressed is how to ensure that a quadratic model of the objective function is positive definite in the null-space of the constrains, while not adversely affecting the convergence of Newton's method nor incurring a significant computational overhead. Numerical evidence to support the theoretical developments is provided.