We present a FORTRAN package of subprograms for minimizing multivariate functions without constraints by a truncated Newton algorithm. The algorithm is especially suited for problems involving a large number of variables. Truncated Newton methods allow approximate, rather than exact, solutions to the Newton equations. Truncation is accomplished in the present version by using the preconditioned Conjugate Gradient algorithm (PCG) to solve approximately the Newton equations. The preconditioner M is factored in PCG using a sparse modified Cholesky factorization based on the Yale Sparse Matrix Package. In this paper we briefly describe the method and provide details for program usage.

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  1. Caliciotti, Andrea; Fasano, Giovanni; Nash, Stephen G.; Roma, Massimo: An adaptive truncation criterion, for linesearch-based truncated Newton methods in large scale nonconvex optimization (2018)
  2. Liang, Yu; Shi, Zhenjun; Chung, Peter W.: A Hessian-free Newton-Raphson method for the configuration of physics systems featured by numerically asymmetric force field (2017)
  3. Cioaca, Alexandru; Sandu, Adrian: An optimization framework to improve 4D-Var data assimilation system performance (2014)
  4. Xie, Dexuan: New solution decomposition and minimization schemes for Poisson-Boltzmann equation in calculation of biomolecular electrostatics (2014)
  5. Cioaca, Alexandru; Alexe, Mihai; Sandu, Adrian: Second-order adjoints for solving PDE-constrained optimization problems (2012)
  6. Jia, Chunxia; Zhu, Detong: An affine scaling interior algorithm via conjugate gradient and Lanczos methods for bound-constrained nonlinear optimization (2011)
  7. Xie, Dexuan; Zarrouk, Mazen G.: Convergence analysis of truncated incomplete Hessian Newton minimization method and application in biomolecular potential energy minimization (2011)
  8. Andrei, Neculai: Accelerated hybrid conjugate gradient algorithm with modified secant condition for unconstrained optimization (2010)
  9. Saad, Yousef; Chelikowsky, James R.; Shontz, Suzanne M.: Numerical methods for electronic structure calculations of materials (2010)
  10. Lukšan, Ladislav; Matonoha, Ctirad; Vlček, Jan: Algorithm 896: LSA: algorithms for large-scale optimization (2009)
  11. Xie, Dexuan; Ni, Qin: An incomplete Hessian Newton minimization method and its application in a chemical database problem (2009)
  12. Wachsmuth, Daniel: Optimal control of the unsteady Navier-Stokes equations (2006)
  13. Xie, Dexuan: An effective compressed sparse preconditioner for large scale biomolecular simulations (2004)
  14. Al-Haik, M. S.; Garmestani, H.; Navon, I. M.: Truncated-Newton training algorithm for neurocomputational viscoplastic model. (2003)
  15. Daescu, Dacian; Navon, I. M.: An analysis of a hybrid optimization method for variational data assimilation (2003)
  16. Li, Zhijin; Navon, I. M.; Hussaini, M. Y.; Le Dimet, F.-X.: Optimal control of cylinder wakes via suction and blowing (2003)
  17. Xie, Dexuan; Singh, Suresh B.; Fluder, Eugene M.; Schlick, Tamar: Principal component analysis combined with truncated-Newton minimization for dimensionality reduction of chemical databases (2003)
  18. Morales, José Luis; Nocedal, Jorge: Enriched methods for large-scale unconstrained optimization (2002)
  19. Xie, Dexuan; Schlick, Tamar: A more lenient stopping rule for line search algorithms (2002)
  20. Xie, Dexuan; Schlick, Tamar: Visualization of chemical databases using the singular value decomposition and truncated-Newton minimization (2000)

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