Abstract
In this paper, a new spectral scaling memoryless Broyden-Fletcher-Goldfarb-Shanno (BFGS) algorithm is developed for solving large scale unconstrained optimization problems, where the scaling parameter is chosen so as to minimize all the eigenvalues of search direction matrices. The search directions in this algorithm are proved to satisfy the approximate Dai-Liao conjugate condition. With this advantage of the search directions, a scaling memoryless BFGS update formula is constructed and an algorithm is developed by incorporating acceleration strategy of line search and restart criterion. Under mild assumptions, global convergence of the algorithm is proved. Numerical tests demonstrate that the developed algorithm is more robust and efficient in solving large scale benchmark test problems than the similar ones in the literature.
Highlights
Optimization models have found wider applications in the fields of engineering and management sciences [1], [2]
A mathematical model of unconstrained optimization problems can be written as min f (x), x ∈ Rn, (1)
In the last round of tests, we report the numerical results in Table 2 as all the seven algorithms are used to solve the benchmark test problems with dimension of over 10000 (DIM)
Summary
Optimization models have found wider applications in the fields of engineering and management sciences [1], [2]. Note that the scaling strategy in the BFGS update formula has been regarded as one of the main approaches to avoid an ill-conditional Bk [9] in (3) It includes two ways: one is to multiply the approximate Hessian matrix by an appropriate scalar before it is updated in the BFGS method. For many large-scale practical optimization models [22], [23], the (scaling) BFGS algorithms like (3) and (4) are often powerless because they are associated with solution of a large-scale system of linear equations Bk dk = −gk , as well as computation and storage of matrices Bk with large sizes Another goal in this paper is to modify the scaling. VOLUME 8, 2020 suggestions for future research, some conclusions are drawn in the last section
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