Title: New Algorithms for A Singly Constrained Class of        
       Quadratic Programs Subject to Lower and Upper Bounds


			  Yu-Hong Dai
	    PO Box 2719, Beijing 100080, PR China 
                       dyh@lsec.cc.ac.cn
                   http://lsec.cc.ac.cn/~dyh

		   co-author: Roger Fletcher

Abstract: 
There are many applications related to singly linearly constrained
quadratic programs subjected to upper and lower bounds. In this  
paper, a new algorithm based on secant approximation is provided
for the case in which the Hessian matrix is diagonal and positive 
definite. To deal with the general case where the Hessian is not 
diagonal, a new efficient projected gradient algorithm is proposed.
The basic features of the projected gradient algorithm are: 1) 
a new formula is used to calculate the initial stepsize; 2) a 
recently-established adaptive nonmonotone line search is incorporated; 
and 3) the optimal stepsize is used by a quadratic interpolation 
if the line search condition fails to be satisfied by the initial stepsize. 
Our numerical experiments on large-scale random test problems and some 
medium-scale quadratic programs arising in the training support vector 
machines demonstrate the usefulness of these algorithms.