Approximation Algorithms for Quadratic Programming

We consider the problem of approximating the global minimum of a general quadratic program (QP) with n variables subject to m ellipsoidal constraints. For m=1, we rigorously show that an -minimizer, where error (0, 1), can be obtained in polynomial time, meaning that the number of arithmetic operations is a polynomial in n, m, and log(1/). For m 2, we present a polynomial-time (1- )-approximation algorithm as well as a semidefinite programming relaxation for this problem. In addition, we present approximation algorithms for solving QP under the box constraints and the assignment polytope constraints.     

非二次泛函极小的正则性

本文考虑向量值函数的泛函用不同于Ａｃｅｒｂｉ－Ｆｕｓｃｏ［１］的方法，重新证明Ｉ（ｕ，Ｇ）的极小的梯度在Ｇ内的处处Ｈｏｌｄｅｒ连续性。本文所用条件稍弱于［１］中的条件。