Relaxed Dual Ascent Method For Equality Constrained Quadratic Convex Optimization

Dual Ascent Method(DAM)is an effective method to solve a class of linearly constrained convex optimization problems,such as in image engineering,signal recognition,computer vision and some other fields.The classical DAM has strict stepsize condition,which increases the difficulty of solving practical problems.He B.S.et al.improve the original algorithm and propose the Self-adaptive Dual Ascent Method(SDAM)with relaxed stepsize condition.According to the literature,SDAM improves the convergence speed of the original DAM and has a wide range of application.Equality constrained quadratic convex optimization(ECQCO)is an important Optimization problem,which has important application in various fields.Since the objective function of ECQCO is a quadratic convex function,it is strong convex,which is beneficial to improving SDAM.Based on SDAM,the stepsize condition is further relaxed and the Relaxed Dual Ascent Method(RDAM)is proposed.Under appropriate assumptions,the convergence of RDAM is proved with the optimality conditions and other related theory.The correlation matrix calibrating problem and synthetic problems verify the relative advantage of calculation performance of RDAM.It can be seen from the numerical experiments that the convergence rate of RDAM is faster than that of DAM-type algorithms and the Customized Proximal Point Algorithm(CPPA)which are commonly used to solve ECQCO under different problem dimensional scalability and calculation stop criteria.Compared with the Augmented Lagrange Method(ALM),RDAM converges slower slightly,but it gives good performance on the problem dimensional scalability,namely as its dimensional scalability grows,because of the self-adaptability of the stepsize,RDAM significantly converges faster,which shows RDAM is more suitable for solving large-scale problems and has obvious computing performance advantage.