Research On Spectral Conjugate Gradient Method And Three-Term Conjugate Gradient Method

With the rapid development of science and technology,the actual problems encountered in life are becoming more and more complex,and the dimensionality and scale are also increasing rapidly.Among many optimization algorithms,the conjugate gradient method requires less storage space and a simple iterative format.It is widely used to find the optimal solution of large-scale unconstrained optimization problems.The spectral conjugate gradient method is a further improvement of the conjugate gradient method.It has relatively stable numerical performance and has received extensive attention and research from scholars.In addition,many scholars have also researched on the three-term conjugate gradient method.This new research idea improves the computing power of the algorithm.Based on the above two different ideas,this thesis proposes three solutions for large-scale unconstrained optimization problems.The specific work is as follows:1.Combining the HS method and the spectral gradient method,under the Wolfe linear search,a search direction with sufficient descent is obtained;using the DL conjugation property,a conjugation condition that can be dynamically adjusted is constructed,a new adaptive spectral HS conjugate gradient method is proposed.It is proved that the algorithm satisfies global convergence under appropriate circumstances.Numerical experiments show that the performance of the MDHS algorithm is better than the HS+ algorithm and the DHS algorithm.2.A three-term conjugate gradient method with a new direction structure is established.Its search direction does not depend on any line search,and each iteration satisfies sufficient descent.Under appropriate conditions,we prove the global convergence of the algorithm.Through numerical experiments on a large number of unconstrained optimization test problems,the results show that the DTTLS algorithm is effective and stable for the given test function,and has good numerical performance in high-dimensional situations.3.A three-term conjugate gradient method for solving large-scale unconstrained optimization problems is proposed.The algorithm retains the important characteristics of the classic PRP method.Under the precise line search,it can be degenerated into the traditional PRP conjugate gradient method.For some specific assumptions,the algorithm satisfies global convergence for most objective functions.Preliminary numerical results show that TTMPRP is suitable for solving large-scale unconstrained optimization problems.