ALGORITHM XXX: SC-SR1: MATLAB SOFTWARE FOR SOLVING SHAPE-CHANGING L-SR1 TRUST-REGION SUBPROBLEMS
Johannes Brust (jbrustucmerced.edu)
Abstract: We present a MATLAB implementation of the shape-changing sym- metric rank-one (SC-SR1) method that solves trust-region subproblems when a limited-memory symmetric rank-one (L-SR1) matrix is used in place of the true Hessian matrix. The method takes advantage of two shape-changing norms [4, 3] to decompose the trust-region subproblem into two separate problems. Using one of the proposed shape-changing norms, the resulting subproblems then have closed-form solutions. In the other proposed norm, one of the resulting subprob- lems has a closed-form solution while the other is easily solvable using techniques that exploit the structure of L-SR1 matrices. Numerical results suggest that the SC-SR1 method is able to solve trust-region subproblems to high accuracy even in the so-called “hard case”.
Keywords: Large-scale unconstrained optimization, nonconvex optimization, trust-region methods, limited-memory quasi-Newton methods, symmetric rank-one update, shape-changing norm
Category 1: Nonlinear Optimization (Unconstrained Optimization )
Citation: Technical Report 2016-2, Wake Forest University, Department of Mathematics, 2016.
Entry Submitted: 07/12/2016
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