A Class of Three-Dimensional Subspace Conjugate Gradient Algorithms for Unconstrained Optimization

In this paper, a three-parameter subspace conjugate gradient method is proposed for solving large-scale unconstrained optimization problems. By minimizing the quadratic approximate model of the objective function on a new special three-dimensional subspace, the embedded parameters are determined and the corresponding algorithm is obtained. The global convergence result of a given method for general nonlinear functions is established under mild assumptions. In numerical experiments, the proposed algorithm is compared with SMCG_NLS and SMCG_Conic, which shows that the given algorithm is robust and efficient.

A new conjugate gradient algorithms using conjugacy condition for solving unconstrained optimization

The primarily objective of this paper which is indicated in the field of conjugate gradient algorithms for unconstrained optimization problems and algorithms is to show the advantage of the new proposed algorithm in comparison with the standard method which is denoted as. Hestenes Stiefel method, as we know the coefficient conjugate parameter is very crucial for this reason, we proposed a simple modification of the coefficient conjugate gradient which is used to derived the new formula for the conjugate gradient update parameter described in this paper. Our new modification is based on the conjugacy situation for nonlinear conjugate gradient methods which is given by the conjugacy condition for nonlinear conjugate gradient methods and added a nonnegative parameter to suggest the new extension of the method. Under mild Wolfe conditions, the global convergence theorem and lemmas are also defined and proved. The proposed method's efficiency is programming and demonstrated by the numerical instances, which were very encouraging.

New scaled algorithm for non-linear conjugate gradients in unconstrained optimization

<p>A new scaled conjugate gradient (SCG) method is proposed throughout this paper, the SCG technique may be a special important generalization conjugate gradient (CG) method, and it is an efficient numerical method for solving nonlinear large scale unconstrained optimization. As a result, we proposed the new SCG method with a strong Wolfe condition (SWC) line search is proposed. The proposed technique's descent property, as well as its global convergence property, are satisfied without the use of any line searches under some suitable assumptions. The proposed technique's efficiency and feasibility are backed up by numerical experiments comparing them to traditional CG techniques.</p>

A Sparse Quasi-Newton Method Based on Automatic Differentiation for Solving Unconstrained Optimization Problems

In our paper, we introduce a sparse and symmetric matrix completion quasi-Newton model using automatic differentiation, for solving unconstrained optimization problems where the sparse structure of the Hessian is available. The proposed method is a kind of matrix completion quasi-Newton method and has some nice properties. Moreover, the presented method keeps the sparsity of the Hessian exactly and satisfies the quasi-Newton equation approximately. Under the usual assumptions, local and superlinear convergence are established. We tested the performance of the method, showing that the new method is effective and superior to matrix completion quasi-Newton updating with the Broyden–Fletcher–Goldfarb–Shanno (BFGS) method and the limited-memory BFGS method.