A new affine scaling interior point algorithm for nonlinear optimization subject to linear equality and inequality constraints

• Published in: Journal of computational and applied mathematics Vol. 161; no. 1; pp. 1 - 25
• Main Author: Zhu, Detong
• Format: Journal Article
• Language: English
• Published: Amsterdam Elsevier B.V 01.12.2003; Elsevier
• Subjects: Affine scaling; Applied sciences; Backtracking step; Calculus of variations and optimal control; Exact sciences and technology; Mathematical analysis; Mathematical programming; Mathematics; Nonmonotonic technique; Numerical analysis; Numerical analysis. Scientific computation; Numerical methods in mathematical programming; Numerical methods in mathematical programming, optimization and calculus of variations; Operational research and scientific management; Operational research. Management science; Sciences and techniques of general use; Trust region method; Nonmonotonic technique; 49 M 40; Affine scaling; Backtracking step; 65 K 05; 90 C 30; Trust region method; Backtracking; Convergence of numerical methods; Numerical analysis; Inequality constraint; Equality constraint; Interior point method; Convergence rate; Constrained optimization; Mathematical programming
• ISSN: 0377-0427; 1879-1778
• DOI: 10.1016/S0377-0427(03)00458-8

In this paper we propose a new interior affine scaling region algorithm with nonmonotonic interior point backtracking technique for nonlinear optimization subject to linear equality and inequality constraints. The trust region subproblem in the proposed algorithm is defined by minimizing a quadratic function subject only to an affine scaling ellipsoidal constraint in a null subspace of the extended equality constraints. Using both trust region strategy and line search technique, the affine scaling trust region subproblem at each iteration generates backtracking interior step to obtain a new accepted step. The global convergence and fast local convergence rate of the proposed algorithm are established under some reasonable conditions. A nonmonotonic criterion should bring about speeding up the convergence progress in some ill-conditioned cases.