IR-SPG

Spectral Projected Gradient with Inexact Restoration

An algorithm for large-scale nonlinear optimization problems with nonconvex constraints, based on the Spectral Projected Gradient method (SPG) with Inexacte Restoration (IR). The basic SPG is highly efficient for solving very large problems when projections on the feasbile set (constraints) are easy. The IR addon extends the algorithm for general nonlinearly constrained problems.

Installation

    devtools::install_github("wol-fi/irspg")

Usage

irspg(X0, objfn, objfn_g, projfn, eqfn, eqfn_g)

where

• X0 ... initial values
• objfn ... objective function
• obfn_g ... gradient of objective function
• projfn ... projection function
• eqfn ... equality constraint (function)
• qfn_g ... gradient of equality constraint

Example

Check the example for an illustrative instruction.

Keywords

non-linear programming, spectral projected gradient, inexact restoration, large-scale optimization

MSC Codes

90C30, 90C26, 65K05, 49K35

Applications

Estimation of Forward-Looking Stock Correaltion Matrices: https://doi.org/10.3390/math10101649

References

Gomes-Ruggiero, M. A., Martínez, J. M., & Santos, S. A. (2009). Spectral projected gradient method with inexact restoration for minimization with nonconvex constraints. SIAM Journal on Scientific Computing, 31(3), 1628-1652. https://doi.org/10.1137/070707828