Inexact proximal methods for weakly convex functions

This paper proposes and develops inexact proximal methods for finding stationary points of the sum of a smooth function and a nonsmooth weakly convex one, where an error is present in the calculation of the proximal mapping of the nonsmooth term. A general framework for finding zeros of a continuous mapping is derived from our previous paper on this subject to establish convergence properties of the inexact proximal point method when the smooth term is vanished and of the inexact proximal gradient method when the smooth term satisfies a descent condition. The inexact proximal point method achieves global convergence with constructive convergence rates when the Moreau envelope of the objective function satisfies the Kurdyka-Lojasiewicz (KL) property. Meanwhile, when the smooth term is twice continuously differentiable with a Lipschitz continuous gradient and a differentiable approximation of the objective function satisfies the KL property, the inexact proximal gradient method achieves the global convergence of iterates with constructive convergence rates.Comment: 26 pages, 3 table

Inexact reduced gradient methods in smooth nonconvex optimization

This paper proposes and develops new line search methods with inexact gradient information for finding stationary points of nonconvex continuously differentiable functions on finite-dimensional spaces. Some abstract convergence results for a broad class of line search methods are reviewed and extended. A general scheme for inexact reduced gradient (IRG) methods with different stepsize selections are proposed to construct sequences of iterates with stationary accumulation points. Convergence results with convergence rates for the developed IRG methods are established under the Kurdyka-Lojasiewicz property. The conducted numerical experiments confirm the efficiency of the proposed algorithms

Globally Convergent Coderivative-Based Generalized Newton Methods in Nonsmooth Optimization

This paper proposes and justifies two globally convergent Newton-type methods to solve unconstrained and constrained problems of nonsmooth optimization by using tools of variational analysis and generalized differentiation. Both methods are coderivative-based and employ generalized Hessians (coderivatives of subgradient mappings) associated with objective functions, which are either of class $\mathcal{C}^{1,1}$, or are represented in the form of convex composite optimization, where one of the terms may be extended-real-valued. The proposed globally convergent algorithms are of two types. The first one extends the damped Newton method and requires positive-definiteness of the generalized Hessians for its well-posedness and efficient performance, while the other algorithm is of {the regularized Newton type} being well-defined when the generalized Hessians are merely positive-semidefinite. The obtained convergence rates for both methods are at least linear, but become superlinear under the semismooth$^*$ property of subgradient mappings. Problems of convex composite optimization are investigated with and without the strong convexity assumption {on smooth parts} of objective functions by implementing the machinery of forward-backward envelopes. Numerical experiments are conducted for Lasso problems and for box constrained quadratic programs with providing performance comparisons of the new algorithms and some other first-order and second-order methods that are highly recognized in nonsmooth optimization.Comment: arXiv admin note: text overlap with arXiv:2101.1055

How Trustworthy are the Existing Performance Evaluations for Basic Vision Tasks?

This paper examines performance evaluation criteria for basic vision tasks involving sets of objects namely, object detection, instance-level segmentation and multi-object tracking. The rankings of algorithms by current criteria fluctuate with different choices of parameters, e.g. Intersection over Union (IoU) threshold, making their evaluations unreliable. More importantly, there is no means to even verify whether we can trust the evaluations of a criterion. This work advocates a notion of trustworthiness for criteria, which requires (i) robustness to parameters for reliability, (ii) contextual meaningfulness in sanity tests, and (iii) consistency with mathematical requirements such as the metric properties. We show that such requirements were overlooked by many widely-used criteria. We also explore alternative criteria using metrics for sets of shapes, and assess them against these requirements to find trustworthy criteria

Synthesis of Al-MCM-41@Ag/TiO2 Nanocomposite and Its Photocatalytic Activity for Degradation of Dibenzothiophene

Mesoporous Al-MCM-41@Ag/TiO2 nanocomposites were synthesized successfully by combining the sol-gel method and hydrothermal treatment, using titanium isopropoxide (TTIP), AgNO3, and Vietnamese bentonite as precursors of Ti, Ag, and Si, respectively. The synthesized materials were well characterized by X-ray powder diffraction (XRD), scanning electron microscopy (SEM), transmission electron microscopy (TEM), N2 adsorption-desorption isotherm measurements, energy dispersive X-ray spectroscopy (EDX), UV-visible diffuse reflectance spectroscopy (UV-Vis/DRS), and X-ray photoelectron spectroscopy (XPS). The photocatalytic activity was evaluated by the photodegradation of dibenzothiophene (DBT) under both UV and visible light irradiation. MCM-41@Ag/TiO2 catalyst exhibited high catalytic activity for the oxidative desulfurization (ODS) of DBT reaching almost 100% conversions at 50°C after 2 h under UV and visible light irradiations. The significant enhanced degradation of DBT over Al-MCM-41@Ag/TiO2 might be due to the synergy effects of high surface area of MCM-41, well-distributed TiO2 anatase, and reduced electron-hole recombination rates due to the dispersion of Ag nanoparticles

Multiple serous membrane effusion caused by primary pericardial mesothelioma

Primary pericardial mesothelioma is an extremely rare cancer with a short survival prognosis. Clinical symptoms are often atypical, and most patients are diagnosed after surgery or at autopsy. We report a case of a 35-year-old female patient with multiple serous membrane effusion for more than 1 year. The patient underwent pericardial, pleural, and peritoneal fluid drainage many times and underwent many laboratory tests to find the cause; however, there was no definitive diagnosis. She was admitted to the hospital because of shortness of breath, cough, and sputum for 5 days. She underwent extensive pericardiectomy to resolve the dyspnea and pericardial surgery to find the cause of the multiple serous membrane effusion. After surgery, her dyspnea was relieved, and the serous effusion gradually decreased

Efficacy of phytotherapy as nutritional supplements in patients with refractory immune thrombocytopenia

Introduction: The management of refractory immune thrombocytopenia (ITP) is challenging and difficult. The treatment was mainly comprised of cytotoxic and immunosuppressed drugs that rarely lead to long-term remission but potentially cause severe and dangerous side effects. Our current study is a retrospective clinical analysis of refractory ITP patients who underwent phytotherapy as nutritional supplements. Methods: A retrospective clinical analysis of 15 refractory immune thrombocytopenia (ITP) patients aged 12–64 with ITP history for more than 24 months before the enrollments. All patients presented with low platelet count (< 30  ×  109/L) and moderate to severe bleeding symptoms such as extensive petechiae, bruising, epistaxis, prolonged menses, rectal bleeding, and hematuria. The patients underwent supportive phytotherapy as nutritional supplements using herbal extracts with hemostatic, immunomodulating, and platelet function augmenting functions Results: The 6-month retrospective clinical evaluation indicated that phytotherapy might offer an effective and safe solution for controlling bleeding symptoms and improving platelet counts for refractory ITP patients. Moreover, phytotherapy also significantly improved patients' red cell count, hemoglobulin, and liver enzyme levels compared to baseline data. Conclusions: In individual cases and economically disadvantaged regions, investigating and applying an appropriate combination of phytotherapy based on scientific knowledge and traditional folk medical experiences might offer an effective, inexpensive, and safe solution for refractory ITP and other bleeding disorders

Steroid glycosides isolated from Paris polyphylla var. chinensis aerial parts and paris saponin II induces G1/S-phase MCF-7 cell cycle arrest

In our previous research on Vietnamese medicinal plants, we found that the ethanolic extract of the aerial parts of Paris polyphylla var. chinensis exhibited cytotoxic effects in vitro in the MCF-7 human cancer cell line. Here, we used combined chromatographic separations to isolate six compounds including a new steroid glycoside, paripoloside A (3), and five known compounds, from the butanol extract of the aerial parts of P. polyphylla. We unambiguously elucidated their structures based on spectroscopic data (proton and carbon-13 nuclear magnetic resonance, heteronuclear single quantum coherence, heteronuclear multiple bond correlation, correlation spectroscopy, and high-resolution electrospray ionization mass spectroscopy data), and chemical reactions. Among the isolated compounds, paris saponin II (PSII) had the strongest cytotoxic effects against MCF-7 breast cancer cells. Interestingly, PSII significantly increased the expression of p53, p21, p27, and Bax protein levels and significantly suppressed the expression of cyclin D1 and retinoblastoma protein. These data suggest that PSII may induce G1/S phase cell cycle arrest and apoptosis pathway development in MCF-7 cells. Furthermore, the MCF-7 breast cancer cells mechanism of PSII was also investigated using molecular docking. Together, our results demonstrate that isolated compounds from P. polyphylla are promising candidates as breast cancer inhibitors