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 \(O(n^{\frac{3}{4}}\log \frac{{({x^0} - l)^T}{s^0} + {(w - {x^0})^T}{t^0}}{\varepsilon })\) iteration complexity bound, which is the best known complexity result for such methods. The numerical results show that our algorithm is effective and promising.

本文提出了一种具有框约束和线性约束（BLCQP）的凸二次规划的宽邻域弧搜索内点算法。该算法沿着近似于整个中心路径的椭圆搜索优化器。假设有一个严格可行的起始点，我们证明该算法具有\（O（n ^ {\ frac {3} {4}} \ log \ frac {{（{x ^ 0}-l）^ T} { s ^ 0} + {（w-{x ^ 0}）^ T} {t ^ 0}} {\ varepsilon}）\）迭代复杂度界限，这是此类方法最著名的复杂度结果。数值结果表明，该算法是有效且有前途的。