Some convergently three-term trust region conjugate gradient algorithms under gradient function non-Lipschitz continuity.

This paper introduces two three-term trust region conjugate gradient algorithms, TT-TR-WP and TT-TR-CG, which are capable of converging under non-Lipschitz continuous gradient functions without any additional conditions. These algorithms possess sufficient descent and trust region properties, and demonstrate global convergence. In order to assess their numerical performance, we compare them with two classical algorithms in terms of restoring noisy gray-scale and color images as well as solving large-scale unconstrained problems. In restoring noisy gray-scale images, we set the performance of TT-TR-WP as the standard, then TT-TR-CG takes around 2.33 times longer. The other algorithms around 2.46 and 2.41 times longer, respectively. In solving the same color images, the proposed algorithms exhibit relative good performance over other algorithms. Additionally, TT-TR-WP and TT-TR-CG are competitive in unconstrained problems, and the former has wide applicability while the latter has strong robustness. Moreover, the proposed algorithms are both more outstanding than the baseline algorithms in terms of applicability and robustness.

vEpiNet: A multimodal interictal epileptiform discharge detection method based on video and electroencephalogram data.

To enhance deep learning-based automated interictal epileptiform discharge (IED) detection, this study proposes a multimodal method, vEpiNet, that leverages video and electroencephalogram (EEG) data. Datasets comprise 24 931 IED (from 484 patients) and 166 094 non-IED 4-second video-EEG segments. The video data is processed by the proposed patient detection method, with frame difference and Simple Keypoints (SKPS) capturing patients' movements. EEG data is processed with EfficientNetV2. The video and EEG features are fused via a multilayer perceptron. We developed a comparative model, termed nEpiNet, to test the effectiveness of the video feature in vEpiNet. The 10-fold cross-validation was used for testing. The 10-fold cross-validation showed high areas under the receiver operating characteristic curve (AUROC) in both models, with a slightly superior AUROC (0.9902) in vEpiNet compared to nEpiNet (0.9878). Moreover, to test the model performance in real-world scenarios, we set a prospective test dataset, containing 215 h of raw video-EEG data from 50 patients. The result shows that the vEpiNet achieves an area under the precision-recall curve (AUPRC) of 0.8623, surpassing nEpiNet's 0.8316. Incorporating video data raises precision from 70% (95% CI, 69.8%-70.2%) to 76.6% (95% CI, 74.9%-78.2%) at 80% sensitivity and reduces false positives by nearly a third, with vEpiNet processing one-hour video-EEG data in 5.7 min on average. Our findings indicate that video data can significantly improve the performance and precision of IED detection, especially in prospective real clinic testing. It suggests that vEpiNet is a clinically viable and effective tool for IED analysis in real-world applications.

A conjugate gradient algorithm for large-scale unconstrained optimization problems and nonlinear equations.

For large-scale unconstrained optimization problems and nonlinear equations, we propose a new three-term conjugate gradient algorithm under the Yuan-Wei-Lu line search technique. It combines the steepest descent method with the famous conjugate gradient algorithm, which utilizes both the relevant function trait and the current point feature. It possesses the following properties: (i) the search direction has a sufficient descent feature and a trust region trait, and (ii) the proposed algorithm globally converges. Numerical results prove that the proposed algorithm is perfect compared with other similar optimization algorithms.

An active-set algorithm for solving large-scale nonsmooth optimization models with box constraints.

It is well known that the active set algorithm is very effective for smooth box constrained optimization. Many achievements have been obtained in this field. We extend the active set method to nonsmooth box constrained optimization problems, using the Moreau-Yosida regularization technique to make the objective function smooth. A limited memory BFGS method is introduced to decrease the workload of the computer. The presented algorithm has these properties: (1) all iterates are feasible and the sequence of objective functions is decreasing; (2) rapid changes in the active set are allowed; (3) the subproblem is a lower dimensional system of linear equations. The global convergence of the new method is established under suitable conditions and numerical results show that the method is effective for large-scale nonsmooth problems (5,000 variables).

The Modified HZ Conjugate Gradient Algorithm for Large-Scale Nonsmooth Optimization.

In this paper, the Hager and Zhang (HZ) conjugate gradient (CG) method and the modified HZ (MHZ) CG method are presented for large-scale nonsmooth convex minimization. Under some mild conditions, convergent results of the proposed methods are established. Numerical results show that the presented methods can be better efficiency for large-scale nonsmooth problems, and several problems are tested (with the maximum dimensions to 100,000 variables).

A Modified BFGS Formula Using a Trust Region Model for Nonsmooth Convex Minimizations.

This paper proposes a modified BFGS formula using a trust region model for solving nonsmooth convex minimizations by using the Moreau-Yosida regularization (smoothing) approach and a new secant equation with a BFGS update formula. Our algorithm uses the function value information and gradient value information to compute the Hessian. The Hessian matrix is updated by the BFGS formula rather than using second-order information of the function, thus decreasing the workload and time involved in the computation. Under suitable conditions, the algorithm converges globally to an optimal solution. Numerical results show that this algorithm can successfully solve nonsmooth unconstrained convex problems.

Two New PRP Conjugate Gradient Algorithms for Minimization Optimization Models.

Two new PRP conjugate Algorithms are proposed in this paper based on two modified PRP conjugate gradient methods: the first algorithm is proposed for solving unconstrained optimization problems, and the second algorithm is proposed for solving nonlinear equations. The first method contains two aspects of information: function value and gradient value. The two methods both possess some good properties, as follows: 1) ßk ≥ 0 2) the search direction has the trust region property without the use of any line search method 3) the search direction has sufficient descent property without the use of any line search method. Under some suitable conditions, we establish the global convergence of the two algorithms. We conduct numerical experiments to evaluate our algorithms. The numerical results indicate that the first algorithm is effective and competitive for solving unconstrained optimization problems and that the second algorithm is effective for solving large-scale nonlinear equations.

A Limited-Memory BFGS Algorithm Based on a Trust-Region Quadratic Model for Large-Scale Nonlinear Equations.

In this paper, a trust-region algorithm is proposed for large-scale nonlinear equations, where the limited-memory BFGS (L-M-BFGS) update matrix is used in the trust-region subproblem to improve the effectiveness of the algorithm for large-scale problems. The global convergence of the presented method is established under suitable conditions. The numerical results of the test problems show that the method is competitive with the norm method.