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Global Convergence of Conjugate Gradient Methods without Line Search

英文关键词:unconstrained optimization  conjugate gradient method  line search  global convergence

中文摘要:

      

英文摘要:

      In this paper, a new steplength formula is proposed for unconstrained optimization, which can determine the step-size only by one step and avoids the line search step. Global convergence of the five well-known conjugate gradient methods with this formula is analyzed, and the corresponding results are as follows: (1) The DY method globally converges for a strongly convex $LC^1$ objective function; (2) The CD method, the FR method, the PRP method and the LS method globally converge for a general, not necessarily convex, $LC^1$ objective function.