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New subroutines for large-scale optimization

Ladislav Luksan(luksan***at***cs.cas.cz)
Ctirad Matonoha(matonoha***at***cs.cas.cz)
Jan Vlcek(vlcek***at***cs.cas.cz)

Abstract: We present fourteen basic FORTRAN subroutines for large-scale unconstrained and box constrained optimization and large-scale systems of nonlinear equations. Subroutines {\tt PLIS} and {\tt PLIP}, intended for dense general optimization problems, are based on limited-memory variable metric methods. Subroutine {\tt PNET}, also intended for dense general optimization problems, is based on an inexact truncated Newton method. Subroutines {\tt PNED} and {\tt PNEC}, intended for sparse general optimization problems, are based on modifications of the discrete Newton method. Subroutines {\tt PSED} and {\tt PSEC}, intended for partially separable optimization problems, are based on partitioned variable metric updates. Subroutine {\tt PSEN}, intended for nonsmooth partially separable optimization problems, is based on partitioned variable metric updates and on an aggregation of subgradients. Subroutines {\tt PGAD} and {\tt PGAC}, intended for sparse nonlinear least squares problems, are based on modifications and corrections of the Gauss-Newton method. Subroutine {\tt PMAX}, intended for minimization of a maximum value (minimax), is based on the primal line-search interior-point method. Subroutine {\tt PSUM}, intended for minimization of a sum of absolute values, is based on the primal trust-region interior-point method. Subroutines {\tt PEQN} and {\tt PEQL}, intended for sparse systems of nonlinear equations, are based on the discrete Newton and the inverse column-update quasi-Newton methods, respectively. Besides the description of methods and codes, we propose computational experiments which demonstrate the efficiency of the proposed algorithms.

Keywords: Large-scale optimization, Large-scale nonsmooth optimization,

Category 1: Optimization Software and Modeling Systems

Category 2: Nonlinear Optimization

Citation: Technical Report No. V999, Institute of Computer Science, Academy of Sciences of the Czech Republic, Prague 2007.

Download: [Postscript][PDF]

Entry Submitted: 07/03/2007
Entry Accepted: 07/03/2007
Entry Last Modified: 07/03/2007

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