A new multipoint symmetric secant method with a dense initial matrix

References

• J. Barzilai and J.M. Borwein, Two-point step size gradient methods, IMA J. Numer. Anal. 8(1) (1988), pp. 141–148.
   Web of Science ®Google Scholar
• J.J. Brust, Large-scale quasi-Newton trust-region methods: High-accuracy solvers, dense initializations, and extensions, Ph.D. diss., UC Merced, 2018.
   Google Scholar
• J. Brust, O. Burdakov, J.B. Erway, and R.F. Marcia, A dense initialization for limited-memory quasi-Newton methods, Comput. Optim. Appl. 74(1) (2019), pp. 121–142.
   Web of Science ®Google Scholar
• J. Brust, O. Burdakov, J. Erway, and R. Marcia, Algorithm 1030: SC-SR1: MATLAB Software for Limited-memory SR1 Trust-region Methods. ACM Trans. Math. Softw. 48(4) (2022), pp. 1–33. https://doi.org/10.1145/3550269.
   Web of Science ®Google Scholar
• J. Brust, J.B. Erway, and R.F. Marcia, On solving L-SR1 trust-region subproblems, Comput. Optim. Appl. 66(2) (2017), pp. 245–266.
   Web of Science ®Google Scholar
• O.P. Burdakov, Methods of the secant type for systems of equations with symmetric Jacobian matrix, Numer. Funct. Anal. Optim. 6(2) (1983), pp. 183–195.
   Web of Science ®Google Scholar
• O.P. Burdakov, L. Gong, S. Zikrin, and Y.-X. Yuan, On efficiently combining limited-memory and trust-region techniques, Math. Program. Comput. 9(1) (2017), pp. 101–134.
   Google Scholar
• O.P. Burdakov, J.M. Martínez, and E.A. Pilotta, A limited-memory multipoint symmetric secant method for bound constrained optimization, Ann. Oper. Res. 117(1-4) (2002), pp. 51–70.
   Web of Science ®Google Scholar
• O. Burdakov and Y.-X. Yuan, On limited-memory methods with shape changing trust region, in Proceedings of the First International Conference on Optimization Methods and Software, 2002, pp. 21.
   Google Scholar
• R.H. Byrd, J. Nocedal, and R.B. Schnabel, Representations of quasi-Newton matrices and their use in limited memory methods, Math. Program. 63(1) (1994), pp. 129–156.
   Google Scholar
• A.R. Conn, N.I.M. Gould, and P.L. Toint, Trust Region Methods, SIAM, 2000.
   Google Scholar
• J.E. Dennis and J.J. Moré, Quasi-Newton methods, motivation and theory, SIAM Rev. 19(1) (1977), pp. 46–89.
   Web of Science ®Google Scholar
• E.D. Dolan and J.J. Moré, Benchmarking optimization software with performance profiles, Math. Program. 91 (2002), pp. 201–213.
   Web of Science ®Google Scholar
• J.B. Erway and R.F. Marcia, Algorithm 943: MSS: Matlab software for L-BFGS trust-region subproblems for large-scale optimization, ACM Trans. Math. Softw. 40(4) (2014), pp. 1–12.
   Web of Science ®Google Scholar
• J.B. Erway and R.F. Marcia, On efficiently computing the eigenvalues of limited-memory quasi-Newton matrices, SIAM. J. Matrix. Anal. Appl. 36 (2015), pp. 1338–1359.
   Web of Science ®Google Scholar
• D.M. Gay, Computing optimal locally constrained steps, SIAM J. Sci. Stat. Comput. 2(2) (1981), pp. 186–197.
   Web of Science ®Google Scholar
• N.I.M. Gould, D. Orban, and P.L. Toint, Cutest: A constrained and unconstrained testing environment with safe threads for mathematical optimization, Comput. Optim. Appl. 60(3) (2015), pp. 545–557.
   Web of Science ®Google Scholar
• N.J. Higham, Accuracy and Stability of Numerical Algorithms, 2nd ed. SIAM, Philadelphia, 2002.
   Google Scholar
• D. J. Higham and N. J. Higham, MATLAB Guide, 3rd ed. SIAM, 2017.
   Google Scholar
• J.J Moré and D.C. Sorensen, Computing a trust region step, SIAM J. Sci. Stat. Comput. 4(3) (1983), pp. 553–572.
   Web of Science ®Google Scholar
• J. Nocedal, Updating quasi-Newton matrices with limited storage, Math. Comput. 35(151) (1980), pp. 773–782.
   Web of Science ®Google Scholar
• J. Nocedal and S. Wright, Numerical Optimization, Springer Science & Business Media, New York, NY, 2006.
   Google Scholar
• M.J.D. Powell, A new algorithm for unconstrained optimization, in Nonlinear Programming, J.B. Rosen, O.L. Mangasarian, and K. Ritter, eds., Academic Press, New York, 1970, pp. 31–65.
   Google Scholar
• R.B. Schnabel, Quasi-Newton methods using multiple secant equations, Tech. Rep., Department of Computer Science, Colorado University, Boulder, 1983.
   Google Scholar