In many large-scale practical problems, Jacobian and Hessian matrices may only be available to an optimizer as linear operators and iterative methods must be used to solve the linear systems. We present recent progress towards the development of a factorization-free method for general nonlinear optimization problems. We will focus on a recently-developed algorithm for linear least-squares problems with linear constraints and show a roadmap for extending the algorithm to nonlinear least-squares problems and general nonlinear optimization problems. We will also present recent numerical results of the linear least-squares algorithm.

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