An affine scaling optimal path method with interior backtracking curvilinear technique for linear constrained optimization

• Published in: Applied mathematics and computation Vol. 207; no. 1; pp. 178 - 196
• Main Authors: Wang, Yunjuan, Zhu, Detong
• Format: Journal Article
• Language: English
• Published: Amsterdam Elsevier Inc 2009; Elsevier
• Subjects: Acceleration of convergence; Affine scaling; Backtracking; Calculus of variations and optimal control; Convergence; Exact sciences and technology; Interior point; Mathematical analysis; Mathematics; Nonmonotonic technique; Numerical analysis; Numerical analysis. Scientific computation; Numerical linear algebra; Numerical methods in mathematical programming, optimization and calculus of variations; Optimal path; Sciences and techniques of general use; Nonmonotonic technique; Backtracking; Optimal path; Interior point; Affine scaling; Convergence; Convergence acceleration; Numerical linear algebra; Decomposition method; Optimization method; Algorithm; Constrained optimization; Convergence speed; Numerical analysis; Algorithm performance; Applied mathematics; Condition number; Convergence rate; Curvature; Mathematical programming
• ISSN: 0096-3003; 1873-5649
• DOI: 10.1016/j.amc.2008.10.023

This paper presents an affine scaling optimal path approach in association with nonmonotonic interior backtracking line search technique for nonlinear optimization subject to linear constraints. We shall employ the eigensystem decomposition and affine scaling mapping to form affine scaling optimal curvilinear path very easily. By using interior backtracking line search technique, each iterate switches to trial step of strict interior feasibility. The nonmonotone criterion is used to speed up the convergence progress in the contours of objective function with large curvature. Theoretical analysis is given which prove that the proposed algorithm is globally convergent and has a local superlinear convergence rate under some reasonable conditions. The results of numerical experiments are reported to show the effectiveness of the proposed algorithm.