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Trust region methods are a class of numerical methods for optimization. Unlike line search type methods where a line search is carried out in each iteration, trust region methods compute a trial step by solving a trust region subproblem where a model function is minimized within a trust region. Due to the trust region constraint, nonconvex models can be used in trust region subproblems, and trust region algorithms can be applied to nonconvex and ill-conditioned problems. Normally it is easier to establish the global convergence of a trust region algorithm than that of its line search counterpart. In the paper, we review recent results on trust region methods for unconstrained optimization, constrained optimization, nonlinear equations and nonlinear least squares, nonsmooth optimization and optimization without derivatives. Results on trust region subproblems and regularization methods are also discussed.

It is crucial to elucidate the impact of climate change on wheat production in China. This article provides a review of the current climate change scenario and its effects on wheat cultivation in China, along with an examination of potential future impacts and possible response strategies. Against the backdrop of climate change, several key trends emerge: increasing temperature during the wheat growing season, raising precipitation, elevated CO 2 concentration, and diminished radiation. Agricultural disasters primarily stem from oscillations in temperature and precipitation, with the northern wheat region being mostly affected. The impact on wheat production is manifested in a reduction in the area under cultivation, with the most rapid reduction in spring wheat, and a shift in the center of cultivation to the west. Furthermore, climate change accelerates the nutritional stage and shortens phenology. Climate change has also led to an increase in yields in the Northeast spring wheat region, the Northern spring wheat region, the Northwest spring wheat region, and the North China winter wheat region, and a decrease in yields in the middle and lower reaches of the Yangtze River winter wheat region, the Southwest winter wheat region, and the South China winter wheat region. To cope with climate change, Chinese wheat can adopt adaptation strategies and measures such as breeding different wheat varieties for different wheat-growing regions, implementing differentiated farmland management measures, promoting regional ecological farmland construction, and establishing scientific monitoring and early warning systems. While future climate change may stimulate wheat yield potential, it could cause climate-induced issues such as weeds, diseases, and pests worsen, thereby posing challenges to the sustainability of farmland. Moreover, it is essential to conduct comprehensive research on pivotal areas such as the microscopic mechanism of climate change and wheat growth, the comprehensive influence of multiple climate factors, and the application of new monitoring and simulation technologies. This will facilitate the advancement of related research and provide invaluable insights.

Aims Increasing evidence indicates that neuroinflammatory and oxidative stress play two pivotal roles in cognitive impairment after surgery. Honokiol (HNK), as an activator of Sirtuin3 (SIRT3), has potential multiple biological functions. The aim of these experiments is to evaluate the effects of HNK on surgery/anesthesia‐induced cognitive decline in mice. Methods Adult C57BL/6 mice received a laparotomy under sevoflurane anesthesia and HNK or SIRT3 inhibitor (3‐TYP) treatment. Cognitive function and locomotor activity of mice were evaluated using fear conditioning test and open field test on postoperative 1 and 3 days. Neuronal apoptosis in CA1 and CA3 area of hippocampus was examined using TUNEL assay. And Western blot was applied to measure the expression of pro‐inflammatory cytokines and SIRT3/SOD2 signaling‐associated proteins in hippocampus. Meanwhile, SIRT3 positive cells were calculated by immunohistochemistry. The mitochondrial membrane potential, malondialdehyde (MDA), and mitochondrial radical oxygen species (mtROS) were detected using standard methods. Results Honokiol attenuated surgery‐induced memory loss and neuronal apoptosis, decreased neuroinflammatory response, and ameliorated oxidative damage in hippocampus. Notably, surgery/anesthesia induced an obviously decrease in hippocampal SIRT3 expression, whereas the HNK increased SIRT3 expression and thus decreased the acetylation of superoxide dismutase 2 (SOD2). However, 3‐TYP treatment inhibited the HNK's rescuing effects. Conclusions These results suggested that activation of SIRT3 by honokiol may attenuate surgery/anesthesia‐induced cognitive impairment in mice through regulation of oxidative stress and neuroinflammatory in hippocampus.

Manifold optimization is ubiquitous in computational and applied mathematics, statistics, engineering, machine learning, physics, chemistry, etc. One of the main challenges usually is the non-convexity of the manifold constraints. By utilizing the geometry of manifold, a large class of constrained optimization problems can be viewed as unconstrained optimization problems on manifold. From this perspective, intrinsic structures, optimality conditions and numerical algorithms for manifold optimization are investigated. Some recent progress on the theoretical results of manifold optimization is also presented.

Background. The potential mechanism of postoperative cognitive impairment is still largely unclear. The activation of NLRP3 inflammasome had been reported to be involved in neurodegenerative diseases, including postoperative cognitive change, and is closely related to mitochondrial ROS and mitophagy. Honokiol (HNK) owns multiple organic protective effects. This study is aimed at observing the neuroprotective effect of HNK in postoperative cognitive change and examining the role of HNK in the regulation of mitophagy and the relationship between these effects and NLRP3 inflammasome activation in mice induced by surgery/anesthesia. Methods. In this study, mice were divided into several groups: control group, surgery group, surgery+HNK group, and surgery+HNK+3-methyladenine (3-MA) group. Hippocampal tissue samples were harvested and used for proinflammatory cytokines, mitochondrial ROS, and malondialdehyde (MDA) assay. The process of mitophagy and the activation of NLRP3 inflammasome were observed by Western blot, immunohistochemistry, and transmission electron microscopy. Results. The results showed that HNK treatment obviously recovered the postoperative decline and enhanced the expressions of LC3-II, Beclin-1, Parkin, and PINK1 at protein levels after surgery/sevoflurane treatment, which are both an autophagy marker and a mitophagy marker. In addition, HNK attenuated mitochondrial structure damage and reduced mtROS and MDA generation, which are closely associated with NLRP3 inflammasome activation. Honokiol-mediated mitophagy inhibited the activation of NLRP3 inflammasome and neuroinflammation in the hippocampus. Using 3-MA, an autophagy inhibitor, the neuroprotective effects of HNK on mitophagy and NLRP3 inflammasome activation were eliminated. Conclusion. These results indicated that HNK-mediated mitophagy ameliorates postoperative cognitive impairment induced by surgery/sevoflurane. This neuroprotective effect may be involved in inhibiting the activation of NLRP3 inflammasome and suppressing inflammatory responses in the hippocampus.

We propose Riemannian preconditioned algorithms for the tensor completion problem via tensor ring decomposition. A new Riemannian metric is developed on the product space of the mode-2 unfolding matrices of the core tensors in tensor ring decomposition. The construction of this metric aims to approximate the Hessian of the cost function by its diagonal blocks, paving the way for various Riemannian optimization methods. Specifically, we propose the Riemannian gradient descent and Riemannian conjugate gradient algorithms. We prove that both algorithms globally converge to a stationary point. In the implementation, we exploit the tensor structure and adopt an economical procedure to avoid large matrix formulation and computation in gradients, which significantly reduces the computational cost. Numerical experiments on various synthetic and real-world datasets—movie ratings, hyperspectral images, and high-dimensional functions—suggest that the proposed algorithms have better or favorably comparable performance to other candidates.

Our purpose of this study is to evaluate the effect and safety of macitentan in the treatment of pulmonary hypertension (PH). We retrieved the safety and efficacy of macitentan treatment for PH using PubMed, the Cochrane Library, EMBASE databases and clinicaltrials.gov. The Cochrane Risk of Bias Tool was used for literature screening and quality assessment. Data analysis was conducted using RevMan 5.4.1 and Stata/SE 15.1 software. Results are presented as standardization mean differences (SMDs) and odds ratio (OR). Meta-analysis of seven randomized controlled trial (RCT) studies and four non-RCT studies with 2769 patients was included, involving 723 in the macitentan group and 599 in the placebo group. The results of the study showed that macitentan had effectively decreased pulmonary vascular resistance (PVR) (SMD = -0.53, 95% CI: -0.77--0.29, p < 0.05), cardiac index (CI) (SMD = 0.60, 95% CI: 0.37-0.83, p < 0.05) and N-terminal pro-brain natriuretic peptide (NT-proBNP) (SMD = -0.22, 95% CI: -0.40--0.03, p < 0.05). Furthermore, macitentan also significantly reduced PVR (SMD = -0.58, 95% CI: -0.80--0.35, p < 0.05), 6-min walk distance (6WMD) (SMD = 0.33, 95% CI: 0.15-0.50, p < 0.05), CI (SMD = 0.48, 95% CI: 0.28-0.69, p < 0.05), mean pulmonary arterial pressure (mPAP) (SMD = -0.43, 95% CI: -0.64--0.23, p < 0.05) and NT-proBNP (SMD = -0.55, 95% CI: -1.07--0.03, p < 0.05) between baseline and follow-up. The adverse reactions to macitentan were mild, with headache, anaemia and bronchitis. Other efficacy and safety outcomes did not reach statistical differences. Macitentan therapy for PH is effective and safe. The effectiveness on PVR, mPAP, mean right atrial pressure (mRAP), mortality and other indicators still needs to be further confirmed.

Inspired by penalty-free approaches for smooth optimization problems, we propose a sequential linearized proximal gradient method (SLPG) for a class of optimization problems with orthogonality constraints and nonsmooth regularization term. This approach alternatively takes tangential steps and normal steps to improve the optimality and feasibility respectively. In SLPG, the orthonormalization process is invoked only once at the last step if high precision for feasibility is needed, showing that main iterations in SLPG are orthonormalization-free. Besides, both the tangential steps and normal steps do not involve the penalty parameter, and thus SLPG is penalty-free and avoids the inefficiency caused by possible inappropriate penalty parameter. We analyze the global convergence properties of SLPG where the tangential steps are inexactly computed. Numerical experiments illustrate the advantages of SLPG when compared with existing first-order methods.

Ordinary differential equations (ODEs) are widely used to model the dynamic behavior of a complex system. Parameter estimation and variable selection for a \"Big System\" with linear ODEs are very challenging due to the need of nonlinear optimization in an ultra-high dimensional parameter space. In this article, we develop a parameter estimation and variable selection method based on the ideas of similarity transformation and separable least squares (SLS). Simulation studies demonstrate that the proposed matrix-based SLS method could be used to estimate the coefficient matrix more accurately and perform variable selection for a linear ODE system with thousands of dimensions and millions of parameters much better than the direct least squares method and the vector-based two-stage method that are currently available. We applied this new method to two real datasets-a yeast cell cycle gene expression dataset with 30 dimensions and 930 unknown parameters and the Standard & Poor 1500 index stock price data with 1250 dimensions and 1,563,750 unknown parameters-to illustrate the utility and numerical performance of the proposed parameter estimation and variable selection method for big systems in practice. Supplementary materials for this article are available online.