A Liu-Storey-type conjugate gradient method for unconstrained minimization problem with application in motion control

An accelerated descent CG algorithm with clustering the eigenvalues for large-scale nonconvex unconstrained optimization and its application in image restoration problems

At present, the conjugate gradient (CG) method of Hager and Zhang (Hager and Zhang, SIAM Journal on Optimization, 16(2005)) is regarded as one of the most effective CG methods for optimization problems. In order to further study the CG method, we develop the Hager and Zhang's CG method and present two modified CG formulas, where the given formulas possess the value information of not only the gradient but also the function. Moreover, the sufficient descent condition will be holden without any line search. The global convergence is established for nonconvex function under suitable conditions. Numerical results show that the proposed methods are competitive to the normal conjugate gradient method.

A modified Polak–Ribière–Polyak conjugate gradient algorithm for nonsmooth convex programs

In this paper, we present two families of modified three-term conjugate gradient methods for solving unconstrained large-scale smooth optimization problems. We show that our new families satisfy the Dai-Liao conjugacy condition and the sufficient descent condition under any line search technique which guarantees the positiveness of ${y_{k}^{T}} s_{k}$. For uniformly convex functions, we indicate that our families are globally convergent under weak-Wolfe-Powell line search technique and standard conditions on the objective function. We also establish a weaker global convergence theorem for general smooth functions under similar assumptions. Our numerical experiments for 260 standard problems and seven other recently developed conjugate gradient methods illustrate that the members of our families are numerically efficient and effective.

In this work, we modify a conjugate gradient (CG) method recently proposed in the literature, where a PRP conjugate gradient method is modified using trust region. Particularly, we propose a hybrid CG method that incorporates the parameters $β^{PRP},$ $β^{FR}$ and $β^{CD},$ and this new search direction satisfies both the trust region feature and the sufficient descent conditions. Furthermore, under suitable conditions the developed method is proved to be globally convergent. The method is tested on some benchmark problems from the literature and numerical results show that it is quite efficient in solving large scale problems.

Conjugate gradient methods are a class of very effective iterative methods for large-scale unconstrained optimization. In this paper, a new Dai-Liao conjugate gradient method for solving large-scale unconstrained optimization problem is proposed. Based on the approximately optimal stepsize for the gradient method, we derive three new choices for the important parameters tk in Dai-Liao conjugate gradient method. The search direction satisfies the sufficient descent condition, and the global convergences of the proposed method for uniformly convex and general functions are proved under some mild conditions. Numerical experiments on a set of test problems from the CUTEst library show that the proposed method is superior to some well-known conjugate gradient methods.

This paper deals with a new nonlinear conjugate gradient method for solving large-scale unconstrained optimization problems. We prove that the new conjugate gradient coefficients  with exact line search is globally convergent. Preliminary numerical results show that  is very efficient when compared to the other classical conjugate gradient coefficients FR,PRP, NPRP, and RMILThis paper deals with a new nonlinear conjugate gradient method for solving large-scale unconstrained optimization problems. We prove that the new conjugate gradient coefficients  with exact line search is globally convergent. Preliminary numerical results show that  is very efficient when compared to the other classical conjugate gradient coefficients FR,PRP, NPRP, and RMIL

The proof of the sufficient descent condition of the Wei–Yao–Liu conjugate gradient method under the strong Wolfe–Powell line search

Hybrid conjugate gradient (CG) techniques are one of the most prominent procedure for obtaining the solution of large-scale unconstrained optimization problems. This is due to its simplicity, global convergence, and low memory requirement. Numerous modifications have been done recently to improve the performance of these methods. In this paper, we proposed new class of hybrid CG coefficients with guaranteed descent under exact line search. Numerical results are presented to illustrate the efficiency of the proposed methodscompared to other classical CG coefficients.

Conjugate gradient (CG) methods have been practically used to solve large-scale unconstrained optimization problems due to their simplicity and low memory storage. In this paper, we proposed a new type of CG coefficients

Recently, the large-scale optimization problems have become a common research topic in the field of evolutionary computation. It is hard to find optimal solutions when solving large-scale multi-objective optimization problems (LSMOPs), due to the ineffectiveness of existing operators. In the other word, the search ability of most existing MOEAs on solving LSMOPs is still weak. To address this issue, an efficient competitive swarm optimizer with a strong exploration ability, denoted as E-CSO, is presented in this paper, which designs a novel three-particle-based particle updating strategy to improve the search efficiency. The experimental results validate the high efficiency and effectiveness of our proposed approach when solving various LSMOPs.

To find a solution of unconstrained optimization problems, we normally use a conjugate gradient (CG) method since it does not cost memory or storage of second derivative like Newton’s method or Broyden–Fletcher–Goldfarb–Shanno (BFGS) method. Recently, a new modification of Polak and Ribiere method was proposed with new restart condition to give a so-call AZPRP method. In this paper, we propose a new modification of AZPRP CG method to solve large-scale unconstrained optimization problems based on a modification of restart condition. The new parameter satisfies the descent property and the global convergence analysis with the strong Wolfe-Powell line search. The numerical results prove that the new CG method is strongly aggressive compared with CG_Descent method. The comparisons are made under a set of more than 140 standard functions from the CUTEst library. The comparison includes number of iterations and CPU time.

Nonlinear conjugate gradient methods for unconstrained optimization problems are used in many aspects of theoretical and applied sciences. They are iterative methods, so at any iteration a step length is computed using a method called line search. In most cases, the sufficient descent condition plays an important role to prove the global convergence of a conjugate gradient method. Due to its outperformance in practical computation, the Polak-Ribière-Polyak (PRP) conjugate gradient method is widely used for solving nonlinear unconstrained optimization problems. However, the sufficient descent condition of PRP has not established without line search yet. In this study, we established the sufficient descent condition without line search based on the conditions 0 < bkPRP £ x bkFR and 1 < bkPRP £mbkFR, where 0 < x < 1 and m > 1. As a result, we found that under certain conditions, the sufficient descent condition is satisfied when the PRP implemented without line search

&lt;p&gt;The conjugate gradient methods are noted to be exceedingly valuable for solving large-scale unconstrained optimization problems since it needn't the storage of matrices. Mostly the parameter conjugate is the focus for conjugate gradient methods. The current paper proposes new methods of parameter of conjugate gradient type to solve problems of large-scale unconstrained optimization. A Hessian approximation in a diagonal matrix form on the basis of second and third-order Taylor series expansion was employed in this study. The sufficient descent property for the proposed algorithm are proved. The new method was converged globally. This new algorithm is found to be competitive to the algorithm of fletcher-reeves (FR) in a number of numerical experiments.&lt;/p&gt;

Some modified Hestenes-Stiefel conjugate gradient algorithms with application in image restoration