Two New Preconditioned Conjugate Gradient Methods for Minimization Problems

In application to general function, each of the conjugate gradient and Quasi-Newton methods has particular advantages disadvantages. Conjugate (CG) techniques are a class unconstrained optimization algorithms with strong local global convergence qualities minimal memory needs. reliable efficient on wide range problems they converge faster than method require fewer function evaluations but have disadvantage requiring substantially more storage if problem is ill-conditioned, may take several iterations. A new been developed, termed preconditioned (PCG) method. It that combines two methods, Quasi-Newton. this work, proposed namely New PCG1 PCG2 solve nonlinear problems. Hestenes-Stiefel (HS) self-scaling symmetric Rank one (SR1), Davidon, Flecher Powell (DFP). The algorithm uses Wolfe line search condition. Numerical comparisons standard show for these algorithms, computational scheme outperforms gradient.