A predictor-correct interior point method is presented for solving convex quadraticprogramming problem with box constraints in this paper. Actually, the method isequivalent to solve a system of equations-the first order optimality conditions of theproblem by decomposing one Newton step with one simplified Newton step, and hasa nice convergent property with high order. Moreover, the center direction generatedby introducing the barrier parameter is used to correct the descent Newton directionsuch that the search direction which consists of the center and Newton direction avoidshitting the board of the feasible region. Therefore, the iterative sequence generated bythe algorithm is remained inside of the feasible region and converges to the optimalsolution. The numerical results for a group of test problems are also given, and haveshown that the algorithm works very efficiently.
首先考虑以下的标准形式的线性规划问题(LP)及其相应的对偶规划(LD):(LP) min c^Tx,s.t.Ax=b,x≥0;(LD) max b^Ty,s.t.A^Ty+s=c,s≥0,其中A∈R^(m×n)(m≤n),c,x,s∈R^n,b,y∈R^m,并且rank(A)=m.以T表示相应于LP和LD中所有可行的x和(y,s)的集合.T^0={(x,y,s):(x,s)>0,(x,y,s)∈T}.由于近年来对线性规划内点方法所进行广泛和深入的研究,人们在理论上对各种不同形式的内点方法的计算复杂性、收敛性质等有较清楚的了解.大量的数值试验表明应用预纠正的原始-对偶内点方法(primal-dual method)
