On Modified Factorizations for Large-Scale Linearly Constrained Optimization
研究了大规模线性约束非线性优化问题中，如何保证目标函数二次模型在约束零空间正定，同时不影响牛顿法收敛且不增加过多计算开销，并提供了数值验证。
We 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 that 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 constraints while neither adversely affecting the convergence of Newton's method nor incurring a significant computational overhead. Numerical evidence to support the theoretical developments is provided.