Carmo Brás

Citation:

Brás, C. P., J. M. Martinez, and M. Raydan. "Large-scale unconstrained optimization using separable cubic modeling and matrix-free subspace minimization." Computational Optimization and Applications. 75 (2020): 169-205.

Abstract:

We present a new algorithm for solving large-scale unconstrained optimization problems that uses cubic models, matrix-free subspace minimization, and secant-type parameters for defining the cubic terms. We also propose and analyze a specialized trust-region strategy to minimize the cubic model on a properly chosen low-dimensional subspace, which is built at each iteration using the Lanczos process. For the convergence analysis we present, as a general framework, a model trust-region subspace algorithm with variable metric and we establish asymptotic as well as complexity convergence results. Preliminary numerical results, on some test functions and also on the well-known disk packing problem, are presented to illustrate the performance of the proposed scheme when solving large-scale problems.

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