A new modification of the quasi-newton method for unconstrained optimization

<p class="MsoNormal" style="text-align: justify;"><span>In this work we propose and analyze a hybrid conjugate gradient (CG) method in which the parameter <!--[if gte mso 9]><xml> <o:OLEObject Type="Embed" ProgID="Equation.3" ShapeID="_x0000_i1025" DrawAspect="Content" ObjectID="_1674222415"> </o:OLEObject> </xml><![endif]-->is computed as a linear combination between Hager-Zhang [HZ] and Dai-Liao [DL] parameters. We use this proposed method to modify BFGS method and to prove the positive definiteness and QN-conditions of the matrix. Theoretical trils confirm that the new search directions aredescent directions under some conditions, as well as, the new search directions areglobally convergent using strong Wolfe conditions. The numerical experiments show that the proposed method is promising and outperforms alternative similar CG-methods using Dolan-Mor'e performance profile. </span><br /><br /></p>

A q-Polak–Ribière–Polyak conjugate gradient algorithm for unconstrained optimization problems

A Polak–Ribière–Polyak (PRP) algorithm is one of the oldest and popular conjugate gradient algorithms for solving nonlinear unconstrained optimization problems. In this paper, we present a q-variant of the PRP (q-PRP) method for which both the sufficient and conjugacy conditions are satisfied at every iteration. The proposed method is convergent globally with standard Wolfe conditions and strong Wolfe conditions. The numerical results show that the proposed method is promising for a set of given test problems with different starting points. Moreover, the method reduces to the classical PRP method as the parameter q approaches 1.

New Investigation for the Liu-Story Scaled Conjugate Gradient Method for Nonlinear Optimization

This article considers modified formulas for the standard conjugate gradient (CG) technique that is planned by Li and Fukushima. A new scalar parameter θkNew for this CG technique of unconstrained optimization is planned. The descent condition and global convergent property are established below using strong Wolfe conditions. Our numerical experiments show that the new proposed algorithms are more stable and economic as compared to some well-known standard CG methods.

A Self-Adjusting Spectral Conjugate Gradient Method for Large-Scale Unconstrained Optimization

This paper presents a hybrid spectral conjugate gradient method for large-scale unconstrained optimization, which possesses a self-adjusting property. Under the standard Wolfe conditions, its global convergence result is established. Preliminary numerical results are reported on a set of large-scale problems in CUTEr to show the convergence and efficiency of the proposed method.