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A family of accelerated hybrid conjugate gradient method for unconstrained optimization and image restoration

JOURNAL OF APPLIED MATHEMATICS AND COMPUTING 2024年第4期70卷 2677-2699页

作者： Wu, Xiaodi Ye, Xiaomin Han, Daolan Guangxi Minzu Univ Sch Math & Phys Nanning 530006 Guangxi Peoples R China

In this paper, a family of hybrid conjugate parameters with restart procedure is proposed. In which, we design a hybrid conjugate parameter by using two hybrid techniques, and set a restart procedure in its search direction according to the conjugate parameter. Under the usual assumptions and the weak Wolfe line search, we prove its sufficient descent property and global convergence. Finally, we choose a specific algorithm from this family and use an acceleration scheme to solve the large-scale unconstrained optimization problems and image restorations. These numerical results show that our algorithm is effective.

关键词： unconstrained optimization Accelerated hybrid conjugate gradient method Restart procedure Global convergence Image restoration 65 Numerical analysis

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A revised Liu-Storey conjugate gradient parameter for unconstrained optimization problems with applications

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ENGINEERING optimization 2025年第3期57卷 624-648页

作者： Salihu, Nasiru Kumam, Poom Yahaya, Mahmoud Muhammad Seangwattana, Thidaporn King Mongkuts Univ Technol Thonburi KMUTT Fac Sci Ctr Excellence Theoret & Computat Sci TaCS CoE Fixed Point Res LabFixed Point Theory & Applicat Bangkok Thailand Modibbo Adama Univ Fac Sci Dept Math Yola Nigeria King Mongkuts Univ Technol Thonburi KMUTT Dept Math Fixed Point Res Lab Bangkok Thailand King Mongkuts Univ Technol North Bangkok Rayong Thailand

Conjugate Gradient (CG) methods are renowned for their efficiency and low memory requirements when solving optimization problems. However, certain formulations of CG methods that switch between two or more CG parameters often overlook specific values that could have been integrated. Moreover, the demonstration of the sufficient descent property in these methods usually relies on a strategy that assumes the possible exclusion of certain function values. To alleviate this assumption, this article introduces a structured Liu-Storey spectral CG method. This method extends the formulation of the spectral Fletcher conjugate descent method, enabling it to maintain fast convergence and inherit a good restart property. Therefore, the method ensures that the sufficient descent property holds without additional requirements and converges globally via some standard assumptions. Additionally, the method proves useful in solving robotic and image reconstruction models. Finally, it demonstrates robustness when compared to some standard algorithms.

关键词： unconstrained optimization spectral conjugate gradient method sufficient descent criteria motion control image recovery

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Collision Detection Between Convex Objects Using Pseudodistance and unconstrained optimization

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IEEE TRANSACTIONS ON ROBOTICS 2025年 41卷 253-268页

作者： Xia, Rilun Wang, Dongming Mou, Chenqi Beihang Univ Sch Math Sci LMIB Beijing 100191 Peoples R China Beihang Univ Sch Artificial Intelligence LMIB Beijing 100191 Peoples R China Sorbonne Univ LIP6 CNRS F-75005 Paris France Beihang Univ Sino French Lab Math Hangzhou Int Innovat Inst Hangzhou 311115 Peoples R China

The problem of collision detection plays an important role in many fields of science and engineering. This article presents a collision detection method for general convex objects bounded by pieces of implicit surfaces. There are two key ideas that underlie our method: one is the introduction of a new kind of pseudodistance, called the $\delta$-distance, for implicitly represented convex objects which has the desired properties of convexity and square differentiability;the other is the use of delta-distance functions to construct a virtual potential field in the real space, so that the problem of collision detection can be reduced to a problem of unconstrained convex optimization. The method is extended and applied to detect whether two objects collide when they are moving continuously along linearly translational trajectories, which is a special case of one of the continuous collision detection subproblems. We have implemented collision detection algorithms in C++ and conducted a large number of experiments, with test examples involving objects modeled by planar, quadric, superquadric, superellipsoidal, and hyperquadric surfaces, as well as pieces of them, in both stationary and linearly translational moving states. The experimental results show that our method has good performance and it is computationally efficient and widely applicable.

关键词： Collision avoidance Convex functions Robots optimization Computational efficiency Ellipsoids Potential energy Trajectory Planning Force Collision detection implicit surface pseudodistance unconstrained optimization

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New non-monotone line search-based adaptive trust region for solving unconstrained optimization problems

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INFOR 2025年

作者： Mirzaei, Seyed Hamzeh Ashrafi, Ali Semnan Univ Fac Math Stat & Comp Sci Dept Math Semnan Iran

This paper deals with the adaptive trust region method with non-monotone line search. We first present a new inexact non-monotone line search and then apply it to the adaptive trust region framework. This method uses the advantage of the line search and non-monotone technique to increase the probability of acceptance of the trial step. The new algorithm exploits an adaptive radius in each iteration that contains first- and second-order information. The properties of global convergence and local superlinearity of the new algorithm are established under standard conditions. Numerical experiments on a set of test functions show the effectiveness of the proposed algorithm.

关键词： unconstrained optimization trust region line search non-monotone technique convergence

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Solving unconstrained optimization using a spectral CG method with restart feature and its application

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JOURNAL OF APPLIED MATHEMATICS AND COMPUTING 2025年第3期71卷 3087-3107页

作者： Ma, Xuejie Yang, Sixing Liu, Pengjie Shen, Liang Li, Minze Guangzhou Huashang Coll Sch Artificial Intelligence Guangzhou 511300 Peoples R China China Univ Min & Technol Sch Math Xuzhou 221116 Peoples R China Xuzhou Med Univ Sch Management Xuzhou 221004 Peoples R China Imperial Coll London Dept Math London SW7 2AZ England

In this study, we present a spectral conjugate gradient method with a built-in restart feature tailored for unconstrained optimization problems. We introduce a selection of bounded spectral parameters, develop an innovative truncation strategy for the RMIL-type conjugate parameter, and establish a novel restart mechanism within our composite search direction. Regardless of the selected bounded spectral parameter and the line search employed, we demonstrate that our proposed search direction meets the sufficient descent property. Furthermore, we establish its global convergence under standard assumptions, including the use of the weak Wolfe line search to generate step size. Numerical comparisons with existing methods highlight the superior performance of our presented methods in addressing unconstrained optimization. Ultimately, we apply the method to solve image restoration problems.

关键词： unconstrained optimization Spectral conjugate gradient method Restart feature Theoretical convergence Image restoration

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Two modified conjugate gradient methods for unconstrained optimization

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optimization METHODS & SOFTWARE 2025年第2期40卷 308-321页

作者： Abd Elhamid, Mehamdia Yacine, Chaib Lab Informat & Math LIM Souk Ahras Algeria Mohamed Cherif Messaadia Univ Souk Ahras 41000 Algeria

Conjugate gradient (CG) methods are a popular class of iterative methods for solving linear systems of equations and nonlinear optimization problems. Motivated by the construction of some modern CG methods, we propose two modified CG methods, named DHS* and DPRP*. Under the strong Wolfe line search (SWLS), the two presented methods are proven to be sufficient descent and globally convergent. Preliminary numerical results show that the DHS* and DPRP* methods are effective for the given test problems.

关键词： unconstrained optimization conjugate gradient method line search sufficient descent global convergence numerical comparisons

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A new diagonal quasi-Newton algorithm for unconstrained optimization problems

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APPLICATIONS OF MATHEMATICS 2024年第4期69卷 501-512页

作者： Nosrati, Mahsa Amini, Keyvan Razi Univ Fac Sci Dept Math Taq e Bostan Kermanshah *** Iran

We present a new diagonal quasi-Newton method for solving unconstrained optimization problems based on the weak secant equation. To control the diagonal elements, the new method uses new criteria to generate the Hessian approximation. We establish the global convergence of the proposed method with the Armijo line search. Numerical results on a collection of standard test problems demonstrate the superiority of the proposed method over several existing diagonal methods.

关键词： unconstrained optimization diagonal quasi-Newton method weak secant equation global convergence

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A new family of hybrid conjugate gradient method for unconstrained optimization and its application to regression analysis

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RAIRO-OPERATIONS RESEARCH 2024年第1期58卷 613-627页

作者： Ben Hanachi, Sabrina Sellami, Badreddine Belloufi, Mohammed Mohamed Cher Messaadia Univ Lab Informat & Math LIM Souk Ahras 41000 Algeria

We know many conjugate gradient algorithms (CG) for solving unconstrained optimization problems. In this paper, based on the three famous Liu-Storey (LS), Fletcher-Reeves (FR) and Polak-Ribiere-Polyak (PRP) conjugate gradient methods, a new hybrid CG method is proposed. Furthermore, the search direction satisfies the sufficient descent condition independent of the line search. Likewise, we prove, under the strong Wolfe line search, the global convergence of the new method. In this respect, numerical experiments are performed and reported, which show that the proposed method is efficient and promising. In virtue of this, the application of the proposed method for solving regression models of COVID-19 is provided.

关键词： unconstrained optimization hybrid conjugate gradient method sufficient descent convex combination global convergence

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TWO DIAGONAL CONJUGATE GRADIENT LIKE METHODS FOR unconstrained optimization

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JOURNAL OF INDUSTRIAL AND MANAGEMENT optimization 2024年第1期20卷 170-187页

作者： Mohammad, Hassan Sulaiman, Ibrahim Mohammed Mamat, Mustafa Bayero Univ Fac Phys Sci Dept Math Sci Numer Optimizat Res Grp Kano 700241 Nigeria Univ Utara Malaysia UUM Sch Quantitat Sci Sintok 06010 Kedah Malaysia UUM Inst Strateg Ind Decis Modelling Sintok 06010 Kedah Malaysia Univ Sultan Zainal Abidin Fac Informat & Comp Terennganu Malaysia

In this paper, we studied a two member family of diagonal conjugate gradient like methods for unconstrained minimization problems. The proposed search directions of the methods are obtained by incorporating a diagonal Hessian approximation approach with the modifications of the Polak-Ribiere-Polyak and Liu-Storey parameters. The resulting directions guarantees the sufficient decrease of the objective function free from any line search. The global convergence of the proposed methods using both the Wolfe and Armijotype line search conditions without the convexity assumption on the function is provided. Furthermore, the R-linear convergence rate of the methods are analyzed under Wolfe line search condition. Numerical experiments demonstrated the performance of the method on general unconstrained minimization problems and image restoration problem.

关键词： unconstrained optimization conjugate gradient methods global convergence numerical results

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An alternative three-dimensional subspace method based on conic model for unconstrained optimization

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RAIRO-OPERATIONS RESEARCH 2024年第1期58卷 775-802页

作者： Wang, Guoxin Pei, Mingyang Wei, Zengxin Yao, Shengwei Guangxi Univ Sch Math & Informat Sci Nanning 530004 Peoples R China Guangxi Univ Nationalities Xiangsihu Coll Nanning 530008 Peoples R China Nanning Normal Univ Coll Math & Stat Nanning 530001 Peoples R China

In this paper, a three-dimensional subspace conjugate gradient method is proposed, in which the search direction is generated by minimizing the approximation model of the objective function in a three-dimensional subspace. The approximation model is not unique and is alternative between quadratic model and conic model by the specific criterions. The strategy of initial stepsize and nonmonotone line search are adopted, and the global convergence of the presented algorithm is established under mild assumptions. In numerical experiments, we use a collection of 80 unconstrained optimization test problems to show the competitive performance of the presented method.

关键词： unconstrained optimization subspace conic model global convergence

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