Approximate solution of system of equations arising in interior-point methods for bound-constrained optimization

Abstract The focus in this paper is interior-point methods for bound-constrained nonlinear optimization, where the system of equations that arise are solved with Newton’s method. There a trade-off between solving Newton systems directly, which give high quality solutions, and many approximate computationally less expensive but lower solutions. We propose partial full solutions to systems. specific solution depends on estimates active inactive constraints at solution. These sets each iteration estimated by basic heuristics. inexpensive, whereas linear needs be size determined estimate In addition, we motivate suggest two Newton-like approaches based an intermediate step consists theoretical setting introduced asymptotic error bounds given. also numerical results investigate performance within beyond framework.