Need realistic test problems for optimization algorithms? This paper describes a test problem generator designed for large-scale unconstrained optimization. The generator enables the creation of both poorly and well-conditioned problems of any size, derived from nonlinear network flow models. The study provides eigenvalue analysis, which bounds the condition number of the Hessian of the objective function. It also offers an example of an efficient preconditioner, using these bounds, is outlined. An eigenvalue analysis provides bounds on the condition number of the Hessian of the objective function and an example of an efficient preconditioner, using these bounds, is outlined. The test problem generator could benefit researchers developing and testing optimization algorithms. The efficient preconditioner offers a practical approach to accelerating convergence in these algorithms.
Published in ACM Transactions on Mathematical Software, this paper on a test problem generator for large-scale unconstrained optimization aligns well with the journal's focus on mathematical software and numerical algorithms. The development of this generator contributes to the journal's goal of facilitating research in optimization by providing tools for testing and comparing different optimization algorithms, providing valuable resources for researchers and practitioners.