A Modified BFGS Formula Using a Trust Region Model for Nonsmooth Convex Minimizations.
Where this comes from
- Record sourced from PubMed, PMID 26501775.
- Also identified by DOI 10.1371/journal.pone.0140606 and PMC identifier 4621044.
- Licence recorded as CC BY.
- The licence permits redistribution, so the abstract is shown in full and the full text is available from the publisher.
Abstract
This paper proposes a modified BFGS formula using a trust region model for solving nonsmooth convex minimizations by using the Moreau-Yosida regularization (smoothing) approach and a new secant equation with a BFGS update formula. Our algorithm uses the function value information and gradient value information to compute the Hessian. The Hessian matrix is updated by the BFGS formula rather than using second-order information of the function, thus decreasing the workload and time involved in the computation. Under suitable conditions, the algorithm converges globally to an optimal solution. Numerical results show that this algorithm can successfully solve nonsmooth unconstrained convex problems.
Medical subject headings
- Algorithms
- Models, Theoretical