An O(<i>n</i><SUP>2</SUP>) active set algorithm for the solution of a parametric quadratic program

作     者：Gómez, MA 

作者机构：Univ A Coruna Fac Econ E-15071 A Coruna Spain 

出 版 物：《NUMERICAL ALGORITHMS》 (Numer. Algorithms)

年 卷 期：1999年第22卷第3-4期

页      面：305-316页

核心收录：

学科分类：07[理学] 070104[理学-应用数学] 0701[理学-数学] 

主　　题：active set methods tax programming models parametric programming 

摘      要：In this paper, an O(n(2)) active set method is presented for minimizing the parametric quadratic function (1/2)x Dx - a x + lambda max(c-gamma x,0) subject to l less than or equal to x less than or equal to b, for all nonnegative values of the parameter lambda . Here, D is a positive diagonal n x n matrix, a and gamma are arbitrary n-vectors, c is an arbitrary scalar, l and b are arbitrary n-vectors, such that l\leq b. An extension of this algorithm is presented for minimizing the parametric function (1/2)x Dx-a x + lambda \gamma x - c\ subject to l less than or equal to x less than or equal to b. It is also shown that these problems arise naturally in a tax programming problem.