Search Results (11)

To address the obstacle-avoidance path-planning requirements of dual-arm robots operating in complex environments, such as chemical laboratories and biomedical workstations, this paper proposes ODSN-RRT (optimization-direction-step-node RRT), an efficient planner based on rapidly-exploring random trees (RRT). ODSN-RRT integrates three key optimization strategies. First, a two-stage sampling-direction strategy employs goal-directed growth until collision, followed by hybrid random-goal expansion. Second, a dynamic safety step-size strategy adapts each extension based on obstacle size and approach angle, enhancing collision detection reliability and search efficiency. Third, an expansion-node optimization strategy generates multiple candidates, selects the best by Euclidean distance to the goal, and employs backtracking to escape local minima, improving path quality while retaining probabilistic completeness. For collision checking in the dual-arm workspace (self and environment), a cylindrical-spherical bounding-volume model simplifies queries to line-line and line-sphere distance calculations, significantly lowering computational overhead. Redundant waypoints are pruned using adaptive segmental interpolation for smoother trajectories. Finally, a master-slave planning scheme decomposes the 14-DOF problem into two 7-DOF sub-problems. Simulations and experiments demonstrate that ODSN-RRT rapidly generates collision-free, high-quality trajectories, confirming its effectiveness and practical applicability. Full article

The primary objective of this article is to enhance the convergence rate of the extragradient method through the careful selection of inertial parameters and the design of a self-adaptive stepsize scheme. We propose an improved version of the extragradient method for approximating a common solution to pseudomonotone equilibrium and fixed-point problems that involve an infinite family of demimetric mappings in real Hilbert spaces. We establish that the iterative sequences generated by our proposed algorithms converge strongly under suitable conditions. These results substantiate the effectiveness of our approach in achieving convergence, marking a significant advancement in the extragradient method. Furthermore, we present several numerical tests to illustrate the practical efficiency of the proposed method, comparing these results with those from established methods to demonstrate the improved convergence rates and solution accuracy achieved through our approach. Full article

This paper explores the iterative approximation of solutions to equilibrium problems and proposes a simple proximal point method for addressing them. We incorporate the golden ratio technique as an extrapolation method, resulting in a two-step iterative process. This method is self-adaptive and does not require any Lipschitz-type conditions for implementation. We present and prove a weak convergence theorem along with a sublinear convergence rate for our method. The results extend some previously published findings from Hilbert spaces to 2-uniformly convex Banach spaces. To demonstrate the effectiveness of the method, we provide several numerical illustrations and compare the results with those from other methods available in the literature. Full article

In this paper, we investigate a class of hierarchical variational inequalities (HVIPs, i.e., strongly monotone variational inequality problems defined on the solution set of multiple-set split common fixed-point problems) with quasi-pseudocontractive mappings in real Hilbert spaces, with special cases being able to be found in many important engineering practical applications, such as image recognizing, signal processing, and machine learning. In order to solve HVIPs of potential application value, inspired by the primal-dual algorithm, we propose a novel accelerated cyclic iterative algorithm that combines the inertial method with a correction term and a self-adaptive step-size technique. Our approach eliminates the need for prior knowledge of the bounded linear operator norm. Under appropriate assumptions, we establish strong convergence of the algorithm. Finally, we apply our novel iterative approximation to solve multiple-set split feasibility problems and verify the effectiveness of the proposed iterative algorithm through numerical results. Full article

In this research paper, we present a new inertial method with a self-adaptive technique for solving the split variational inclusion and fixed point problems in real Hilbert spaces. The algorithm is designed to choose the optimal choice of the inertial term at every iteration, and the stepsize is defined self-adaptively without a prior estimate of the Lipschitz constant. A convergence theorem is demonstrated to be strong even under lenient conditions and to showcase the suggested method’s efficiency and precision. Some numerical tests are given. Moreover, the significance of the proposed method is demonstrated through its application to an image reconstruction issue. Full article

Symmetry plays an important role in solving practical problems of applied science, especially in algorithm innovation. In this paper, we propose what we call the self-adaptive inertial-like proximal point algorithms for solving the split common null point problem, which use a new inertial structure to avoid the traditional convergence condition in general inertial methods and avoid computing the norm of the difference between $x_n$ and $x_{n-1}$ before choosing the inertial parameter. In addition, the selection of the step-sizes in the inertial-like proximal point algorithms does not need prior knowledge of operator norms. Numerical experiments are presented to illustrate the performance of the algorithms. The proposed algorithms provide enlightenment for the further development of applied science in order to dig deep into symmetry under the background of technological innovation. Full article

Lévy flights random walk is one of key parts in the cuckoo search (CS) algorithm to update individuals. The standard CS algorithm adopts the constant scale factor for this random walk. This paper proposed an improved beta distribution cuckoo search (IBCS) for this factor in the CS algorithm. In terms of local characteristics, the proposed algorithm makes the scale factor of the step size in Lévy flights showing beta distribution in the evolutionary process. In terms of the overall situation, the scale factor shows the exponential decay trend in the process. The proposed algorithm makes full use of the advantages of the two improvement strategies. The test results show that the proposed strategy is better than the standard CS algorithm or others improved by a single improvement strategy, such as improved CS (ICS) and beta distribution CS (BCS). For the six benchmark test functions of 30 dimensions, the average rankings of the CS, ICS, BCS, and IBCS algorithms are 3.67, 2.67, 1.5, and 1.17, respectively. For the six benchmark test functions of 50 dimensions, moreover, the average rankings of the CS, ICS, BCS, and IBCS algorithms are 2.83, 2.5, 1.67, and 1.0, respectively. Confirmed by our case study, the performance of the ABCS algorithm was better than that of standard CS, ICS or BCS algorithms in the process of EDM. For example, under the single-objective optimization convergence of MRR, the iteration number (13 iterations) of the CS algorithm for the input process parameters, such as discharge current, pulse-on time, pulse-off time, and servo voltage, was twice that (6 iterations) of the IBCS algorithm. Similar, the iteration number (17 iterations) of BCS algorithm for these parameters was twice that (8 iterations) of the IBCS algorithm under the single-objective optimization convergence of Ra. Therefore, it strengthens the CS algorithm’s accuracy and convergence speed. Full article

Studying Bregman distance iterative methods for solving optimization problems has become an important and very interesting topic because of the numerous applications of the Bregman distance techniques. These applications are based on the type of convex functions associated with the Bregman distance. In this paper, two different extragraident methods were proposed for studying pseudomonotone variational inequality problems using Bregman distance in real Hilbert spaces. The first algorithm uses a fixed stepsize which depends on a prior estimate of the Lipschitz constant of the cost operator. The second algorithm uses a self-adaptive stepsize which does not require prior estimate of the Lipschitz constant of the cost operator. Some convergence results were proved for approximating the solutions of pseudomonotone variational inequality problem under standard assumptions. Moreso, some numerical experiments were also given to illustrate the performance of the proposed algorithms using different convex functions such as the Shannon entropy and the Burg entropy. In addition, an application of the result to a signal processing problem is also presented. Full article

We introduce a new projection and contraction method with inertial and self-adaptive techniques for solving variational inequalities and split common fixed point problems in real Hilbert spaces. The stepsize of the algorithm is selected via a self-adaptive method and does not require prior estimate of norm of the bounded linear operator. More so, the cost operator of the variational inequalities does not necessarily needs to satisfies Lipschitz condition. We prove a strong convergence result under some mild conditions and provide an application of our result to split common null point problems. Some numerical experiments are reported to illustrate the performance of the algorithm and compare with some existing methods. Full article

The Co-frequency Co-time Full Duplex (CCFD) is a key concept in 5G wireless communication networks. The biggest challenge for CCFD wireless communication is the strong self-interference (SI) from near-end transceivers. Aiming at cancelling the SI of near-end transceivers in CCFD systems in the radio frequency (RF) domain, a novel time-varying Least Mean Square (LMS) adaptive filtering algorithm which is based on step-size parameters gradually decrease with time varying called the DTV-LMS algorithm is proposed in this paper. The proposed DTV-LMS algorithm in this paper establishes the non-linear relationship between step factor and the evolved arct-angent function, and using the relationship between the time parameter and error signal correlation value to coordinately control the step factor to be updated. This algorithm maintains a low computational complexity. Simultaneously, the DTV-LMS algorithm can also attain the ideal characteristics, including the interference cancellation ratio (ICR), convergence speed, and channel tracking, so that the SI signal in the RF domain of a full duplex system can be effectively cancelled. The analysis and simulation results show that the ICR in the RF domain of the proposed algorithm is higher than that in the compared algorithms and have a faster convergence speed. At the same time, the channel tracking capability has also been significantly enhanced in CCFD systems. Full article

We investigate the split variational inclusion problem in Hilbert spaces. We propose efficient algorithms in which, in each iteration, the stepsize is chosen self-adaptive, and proves weak and strong convergence theorems. We provide numerical experiments to validate the theoretical results for solving the split variational inclusion problem as well as the comparison to algorithms defined by Byrne et al. and Chuang, respectively. It is shown that the proposed algorithms outrun other algorithms via numerical experiments. As applications, we apply our method to compressed sensing in signal recovery. The proposed methods have as a main advantage that the computation of the Lipschitz constants for the gradient of functions is dropped in generating the sequences. Full article