A trust region and affine scaling interior point method for nonconvex minimization with linear inequality constraints

Citation
Tf. Coleman et Yy. Li, A trust region and affine scaling interior point method for nonconvex minimization with linear inequality constraints, MATH PROGR, 88(1), 2000, pp. 1-31
Citations number
27
Language
INGLESE
art.tipo
Article
Categorie Soggetti
Mathematics
Journal title
MATHEMATICAL PROGRAMMING
ISSN journal
0025-5610 → ACNP
Volume
88
Issue
1
Year of publication
2000
Pages
1 - 31
Database
ISI
SICI code
0025-5610(200006)88:1<1:ATRAAS>2.0.ZU;2-I
Abstract
A trust region and affine scaling interior point method (TRAM) is proposed for a general nonlinear minimization with linear inequality constraints [8] . In the proposed approach, a Newton step is derived from the complementari ty conditions. Based on this Newton step, a trust region subproblem is form ed, and the original objective function is monotonically decreased. Explici t sufficient decrease conditions are proposed for satisfying the first orde r and second order necessary conditions. The objective of this paper is to establish global and local convergence pr operties of the proposed trust region and affine scaling interior point met hod. It is shown that the proposed explicit decrease conditions are suffici ent for satisfy complementarity, dual feasibility and second order necessar y conditions respectively. It is also established that a trust region solut ion is asymptotically in the interior of the proposed trust region subprobl em and a properly damped trust region step can achieve quadratic convergenc e.