Hybrid Conjugate Gradient Method Research Articles

A New Hybrid Conjugate Gradient Method with Guaranteed Descent for Unconstraint Optimization

The conjugate gradient method an efficient technique for solving the unconstrained optimization problem. In this paper, we propose a new hybrid nonlinear conjugate gradient methods, which have the descent at every iteration and globally convergence properties under certain conditions. The numerical results show that new hybrid method are efficient for the given test problems.

New Hybrid Conjugate Gradient Method with Global Convergence Properties for Unconstrained Optimization

Nonlinear conjugate gradient (CG) method holds an important role in solving large-scale unconstrained optimization problems. In this paper, we suggest a new modification of CG coefficient that satisfies sufficient descent condition and possesses global convergence property under strong Wolfe line search. The numerical results show that our new method is more efficient compared with other CG formulas tested.

A Five-term Hybrid Conjugate Gradient Method with Global Convergence and Descent Properties for Unconstrained Optimization Problems

A Five-term Hybrid Conjugate Gradient Method with Global Convergence and Descent Properties for Unconstrained Optimization Problems

A compressive hybrid conjugate gradient image recovery approach for radial MRI

ABSTRACTThis paper investigates an efficient compressed sensing (CS) approach that can be used to reconstruct radial magnetic resonance (MR) images from under-sampled measurements. In this approach, we propose a hybrid conjugate gradient (CG) method with a hybrid update parameter to optimize the CS cost function. With detailed mathematical proofs, the proposed CG method has proved to have sufficient descent and global convergence properties. In order to show efficiency of the proposed approach, experiments using a phantom and a living mouse cardiac example are carried out. Compared with two other widely used compressive CG approaches with undersampling rates from 5% to 20%, the proposed approach achieves better image quality and requires less running time. Meanwhile, the proposed H-CG approach can improve the robustness of magnetic resonance imaging image recovery above existing compressive CG approaches.

A descent hybrid conjugate gradient method based on the memoryless BFGS update

In this work, we present a new hybrid conjugate gradient method based on the approach of the convex hybridization of the conjugate gradient update parameters of DY and HS+, adapting a quasi-Newton philosophy. The computation of the hybrization parameter is obtained by minimizing the distance between the hybrid conjugate gradient direction and the self-scaling memoryless BFGS direction. Furthermore, a significant property of our proposed method is that it ensures sufficient descent independent of the accuracy of the line search. The global convergence of the proposed method is established provided that the line search satisfies the Wolfe conditions. Our numerical experiments on a set of unconstrained optimization test problems from the CUTEr collection indicate that our proposed method is preferable and in general superior to classic conjugate gradient methods in terms of efficiency and robustness.

Global convergence analysis of a new hybrid conjugate gradient method for unconstrained optimization problems

In this paper, we propose a new hybrid conjugate gradient method for unconstrained optimization problems. The proposed method comprises of beta (DY), beta (WHY), beta (RAMI) and beta (New). The beta (New) was constructed purposely for this proposed hybrid method.The method possesses sufficient descent property irrespective of the line search. Under Strong Wolfe-Powell line search, we proved that the method is globally convergent. Numerical experimentation shows the effectiveness and robustness of the proposed method when compare with some hybrid as well as some modified conjugate gradient methods.

Performance comparison of a new hybrid conjugate gradient method under exact and inexact line searches

Conjugate gradient (CG) method is one of iterative techniques prominently used in solving unconstrained optimization problems due to its simplicity, low memory storage, and good convergence analysis. This paper presents a new hybrid conjugate gradient method, named NRM1 method. The method is analyzed under the exact and inexact line searches in given conditions. Theoretically, proofs show that the NRM1 method satisfies the sufficient descent condition with both line searches. The computational result indicates that NRM1 method is capable in solving the standard unconstrained optimization problems used. On the other hand, the NRM1 method performs better under inexact line search compared with exact line search.

A modified quadratic hybridization of Polak-Ribiere-Polyak and Fletcher-Reeves conjugate gradient method for unconstrained optimization problems

This article presents a modified quadratic hybridization of the Polak–Ribiere–Polyak and Fletcher–Reeves conjugate gradient method for solving unconstrained optimization problems. Global convergence, with the strong Wolfe line search conditions, of the proposed quadratic hybrid conjugate gradient method is established. We also report some numerical results to show the competitiveness of the new hybrid method.

New hybrid conjugate gradient method as a convex combination of LS and CD methods

A new hybrid conjugate gradient algorithm is considered. The conjugate gradient parameter βk is computed as a convex combination of βCD k and βLS k. The parameter θk is computed in such a way that the conjugacy condition is satisfied. The strong Wolfe line search conditions are used. Numerical comparisons show that the present hybrid conjugate gradient algorithm often behaves better than some known algorithms.

New hybrid conjugate gradient methods with the generalized Wolfe line search.

The conjugate gradient method was an efficient technique for solving the unconstrained optimization problem. In this paper, we made a linear combination with parameters βk of the DY method and the HS method, and putted forward the hybrid method of DY and HS. We also proposed the hybrid of FR and PRP by the same mean. Additionally, to present the two hybrid methods, we promoted the Wolfe line search respectively to compute the step size αk of the two hybrid methods. With the new Wolfe line search, the two hybrid methods had descent property and global convergence property of the two hybrid methods that can also be proved.

New hybrid conjugate gradient method as a convex combination of FR and PRP methods

We consider a newhybrid conjugate gradient algorithm,which is obtained fromthe algorithmof Fletcher-Reeves, and the algorithmof Polak-Ribi?re-Polyak. Numerical comparisons show that the present hybrid conjugate gradient algorithm often behaves better than some known algorithms.

Fast Level-Set-Based Inverse Lithography Algorithm for Process Robustness Improvement and Its Application

Inverse lithography technology (ILT) is one of the promising resolution enhancement techniques (RETs), as the advanced integrated circuits (IC) technology nodes still use the 193 nm light source. Among all the algorithms for ILT, the level-set-based ILT (LSB-ILT) is a feasible choice with good production result in practice. However, existing ILT algorithms optimize masks at nominal process condition without giving sufficient attention to the process variations, and thus the optimized masks show poor performance with focus and dose variations. In this paper, we put forward a new LSB-ILT algorithm for process robustness improvement with fast convergence. In order to account for the process variations in the optimization, we adopt a new form of the cost function by adding the objective function of process variation band (PV band) to the nominal cost. We also adopt the hybrid conjugate gradient (CG) method to reduce the runtime of the algorithm. We perform experiments on ICCAD 2013 benchmarks and the results show that our algorithm outperforms the top two winners of the ICCAD 2013 contest by 6.5%. We also adopt the attenuated phase shift mask (att-PSM) in the experiment with test cases from industry. The results show that our new algorithm has a fast convergence speed and reduces the process manufacturability index (PMI) by 38.77% compared with the LSB-ILT algorithm without the consideration of PV band.

A nonmonotone hybrid conjugate gradient method for unconstrained optimization

A nonmonotone hybrid conjugate gradient method is proposed, in which the technique of the nonmonotone Wolfe line search is used. Under mild assumptions, we prove the global convergence and linear convergence rate of the method. Numerical experiments are reported.

A Class New Hybrid Conjugate Gradient Method for Unconstrained Optimization

In this paper, A class new parameter conjugate gradient method and a new hybrid conjugate gradient method are proposed. The global convergence of the algorithms are proved under the Wolfe line search without the descent condition. Numerical experiments show that the hybrid conjugate gradient algorithm is recommendable.

An Efficient Hybrid Conjugate Gradient Method with the Strong Wolfe-Powell Line Search

Conjugate gradient (CG) method is an interesting tool to solve optimization problems in many fields, such as design, economics, physics, and engineering. In this paper, we depict a new hybrid of CG method which relates to the famous Polak-Ribière-Polyak (PRP) formula. It reveals a solution for the PRP case which is not globally convergent with the strong Wolfe-Powell (SWP) line search. The new formula possesses the sufficient descent condition and the global convergent properties. In addition, we further explained about the cases where PRP method failed with SWP line search. Furthermore, we provide numerical computations for the new hybrid CG method which is almost better than other related PRP formulas in both the number of iterations and the CPU time under some standard test functions.

A hybridization of the Hestenes–Stiefel and Dai–Yuan conjugate gradient methods based on a least-squares approach

Following Andrei's approach of combining the conjugate gradient parameters convexly, a hybridization of the Hestenes–Stiefel (HS) and Dai–Yuan conjugate gradient (CG) methods is proposed. The hybridization parameter is computed by solving the least-squares problem of minimizing the distance between search directions of the hybrid method and a three-term conjugate gradient method proposed by Zhang et al. which possesses the sufficient descent property. Also, Powell's non-negative restriction of the HS CG parameter is employed in the hybrid method. A brief global convergence analysis is made without convexity assumption on the objective function. Comparative testing results are reported; they demonstrate efficiency of the proposed hybrid CG method in the sense of the Dolan–Moré performance profile.

A hybrid conjugate gradient method with descent property for unconstrained optimization

In this paper, based on some famous previous conjugate gradient methods, a new hybrid conjugate gradient method was presented for unconstrained optimization. The proposed method can generate decent directions at every iteration, moreover, this property is independent of the steplength line search. Under the Wolfe line search, the proposed method possesses global convergence. Medium-scale numerical experiments and their performance profiles are reported, which show that the proposed method is promising.

New hybrid conjugate gradient method for unconstrained optimization

In this paper, we propose a new hybrid conjugate gradient method for solving unconstrained optimization problems. The proposed method can be viewed as a convex combination of Liu–Storey method and Dai–Yuan method. An remarkable property is that the search direction of this method not only satisfies the famous D–L conjugacy condition, but also accords with the Newton direction with suitable condition. Furthermore, this property is not dependent on any line searches. Under the strong Wolfe line searches, the global convergence of the proposed method is established. Preliminary numerical results also show that our method is robust and effective.

New Iterative Conjugate Gradient Method for Nonlinear Unconstrained Optimization Using Homptopy Technique

A new hybrid conjugate gradient method for unconstrained optimization by using homotopy formula , we computed the parameter as aconvex combination of (Polak-Ribiere (PR))(9) and (Al-Bayati and Al-Assady (BA))(1).

Comments on “A hybrid conjugate gradient method based on a quadratic relaxation of the Dai-Yuan hybrid conjugate gradient parameter”

In this note, we show that the assumption condition (3.3) in Theorem 3.2 of Babaie-Kafaki can be deleted. As mentioned in Babaie-Kafaki, it is not appropriate to consider condition (3.3) as an assumption. Throughout, we use the same notations and equation numbers as in Babaie-Kafaki.