Differential-Algebraic Equations Model for Quadratic Programming

Abstract

A differential-algebraic equations (DAEs) model for solving convex quadratic programming (CQP) is studied in this paper. By using Frisch's logarithmic barrier function, the DAEs model is established and the corresponding relationships of the solutions to the proposed DAEs with the CQP problems is analyzed in details here. All the results shows that this new model is different from traditional optimization algorithms which tries to find optimal solutions by the classical discrete iterated sequence points as well as different from neural network method based on the ODEs which tries to find the optimal solutions by tracking trajectories of a set of ordinary differential equation systems. It is well-known that different numerical schemes to DAEs algorithm can lead to new algorithms or some classical iterated algorithms, for instance, the path-following interior point algorithm could be conducted by a scheme of the proposed DAEs algorithm. So, in this aspect, the conventional interior point method can be viewed as a special case of the new DAEs method. Hence, this DAEs model provides a promising alternative approach for solving convex quadratic programming problems.