Bi-affine scaling iterative method for convex quadratic programming with bound constraints

• Published in: Mathematics and computers in simulation Vol. 226; pp. 373 - 382
• Main Authors: Yue, Hongwei, Shen, Peiping
• Format: Journal Article
• Language: English
• Published: Elsevier B.V 01.12.2024
• Subjects: Affine scaling; Bound constraints; Convex quadratic programming; Interior-point algorithm; Convex quadratic programming; Bound constraints; Interior-point algorithm; Affine scaling
• ISSN: 0378-4754
• DOI: 10.1016/j.matcom.2024.07.013

To solve general convex quadratic programming problems with bound constraints, this paper proposes a new interior point iterative method that is easy to be implemented. The method exhibits a simple and sufficiently smooth search direction, and possesses the characteristics of affine scaling. Under the limited optimal stepsize rule, starting from an arbitrary interior point, any accumulation point of the generated sequence is an optimal solution of the corresponding problem. Furthermore, due to the absence of introducing dual variables and solving equations, the proposed method is more suitable for solving large-scale problems. Preliminary numerical results indicate that the new method has advantages in terms of both efficiency and accuracy. •Its search direction is simple and sufficiently smooth, meanwhile possesses the features of affine scaling method.•Since it does not require the introduction of dual variables or solving linear equation systems, the new method is more suitable for solving the large-scale problems.•The conditions for ensuring global convergence are relatively weak.•Preliminary numerical results indicate that the new method has advantages in terms of both efficiency and accuracy.