A symmetric rank-one Quasi-Newton method using negative curvature directions
Öztoprak, Figen and Birbil, Ş. İlker (2009) A symmetric rank-one Quasi-Newton method using negative curvature directions. (Submitted)
We propose a quasi-Newton method that uses negative curvature directions for solving unconstrained optimization problems. In this method, the symmetric rank-one (SR1) rule is used to update the Hessian approximation. The SR1 update rule is known to have a good numerical performance; however, it does not guarantee positive definiteness of the updated matrix. We first discuss the details of the proposed algorithm and then concentrate on its numerical efficiency. Our extensive computational study on small-to-moderate size well-known benchmark problems shows the potential of the proposed method from different angles, such as; its second order convergence behavior, its exceeding performance when compared to two other existing packages, and its computation profile illustrating the possible bottlenecks in the execution time. We then conclude the paper with the first and second order convergence analysis of the proposed method.
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