ZIB

Hits per page

hits 1 - 3 | 3 hits

Sorting

Electronic Resource

Failure of global convergence for a class of interior point methods for nonlinear programming (2000)

Wächter, Andreas ; Biegler, Lorenz T.

Springer

Mathematical programming 88 (2000), S. 565-574

add to mindlist on the mindlist

Details

ISSN: 1436-4646

Keywords: Key words: nonlinear optimization – interior point methods – global convergence – Newton’s method ; Mathematics Subject Classification (1991): 65K05, 90G30, 90G51

Source: Springer Online Journal Archives 1860-2000

Topics: Computer Science , Mathematics

Notes: Abstract. Using a simple analytical example, we demonstrate that a class of interior point methods for general nonlinear programming, including some current methods, is not globally convergent. It is shown that those algorithms produce limit points that are neither feasible nor stationary points of some measure of the constraint violation, when applied to a well-posed problem.

Type of Medium: Electronic Resource

URL: http://dx.doi.org/10.1007/PL00011386

Permalink

Library	Location	Call Number	Volume/Issue/Year	Availability

Others were also interested in ...

Paper (German National Licenses)

Fulltext

Unknown

Inertia Revealing Preconditioning For Large-Scale Nonconvex Constrained Optimization (2007)

Schenk, Olaf ; Wächter, Andreas ; Weiser, Martin

add to mindlist on the mindlist

Details

Publication Date: 2019-01-29

Description: Fast nonlinear programming methods following the all-at-once approach usually employ Newton's method for solving linearized Karush-Kuhn-Tucker (KKT) systems. In nonconvex problems, the Newton direction is only guaranteed to be a descent direction if the Hessian of the Lagrange function is positive definite on the nullspace of the active constraints, otherwise some modifications to Newton's method are necessary. This condition can be verified using the signs of the KKT's eigenvalues (inertia), which are usually available from direct solvers for the arising linear saddle point problems. Iterative solvers are mandatory for very large-scale problems, but in general do not provide the inertia. Here we present a preconditioner based on a multilevel incomplete $LBL^T$ factorization, from which an approximation of the inertia can be obtained. The suitability of the heuristics for application in optimization methods is verified on an interior point method applied to the CUTE and COPS test problems, on large-scale 3D PDE-constrained optimal control problems, as well as 3D PDE-constrained optimization in biomedical cancer hyperthermia treatment planning. The efficiency of the preconditioner is demonstrated on convex and nonconvex problems with $150^3$ state variables and $150^2$ control variables, both subject to bound constraints.

Keywords: ddc:510

Language: English

Type: reportzib , doc-type:preprint

Format: application/pdf

Permalink