大规模严格凸二次规划问题一个新算法

A NEW ALOGRITHM OF LARGE SCALE STRICT CONVEX QUADRATIC PROGRAM

根据广义乘子法的思想，将具有等式约束和非负约束的凸二次规划问题转化为只有非负约束的简单凸二次规划，通过解简单凸二次规划来得到解等式约束和非负约束的凸二次规划新算法，新算法不用求逆矩阵，这样可充分保持矩阵的稀疏性，用来解大规模稀疏问题．数值结果表明：在微机４８６／３３上就能解较大规模的凸二次规划．

This paper applies generalized multipler method to translate convex quadratic programs with equal constraints and non negative constraints into simple convex quadratic programs with non negative constraints.The new algorithm is gotten by solving the simple quadratic program.It avoids the computation of inverse matrix and exploits sparsity structure in the matrix of the quadratic form.The results of numerical experiments show the effectiveness of the algorithm on large scale problems.