A wide neighborhood arc-search interior-point algorithm for convex quadratic programming with box constraints and linear constraints

作者：Zhang, Mingwang; Huang, Kun^*; Lv, Yanli

来源：OPTIMIZATION AND ENGINEERING, 2022, 23(2): 1117-1137.

DOI：10.1007/s11081-021-09626-y

• Convex programming
• Interior-point methods
• Arc-search
• Box constraints
• Polynomial complexity

In this paper, a wide neighborhood arc-search interior-point algorithm for convex quadratic programming with box constrains and linear constraints (BLCQP) is presented. The algorithm searches the optimizers along the ellipses that approximate the entire central path. Assuming a strictly feasible initial point is available, we show that the algorithm has O(n(3/4) log (x(0)-l)(T) s(0)+(w-x(0))(T) t(0)/epsilon) iteration complexity bound, which is the best known complexity result for such methods. The numerical results show that our algorithm is effective and promising.