A Generalized Newton Method for Subgradient Systems

This paper proposes and develops a new Newton-type algorithm to solve subdifferential inclusions defined by subgradients of extended-real-valued prox-regular functions. The proposed algorithm is formulated in terms of the second-order subdifferential of such functions that enjoys extensive calculus rules and can be efficiently computed for broad classes of extended-real-valued functions. Based on this and on metric regularity and subregularity properties of subgradient mappings, we establish verifiable conditions ensuring well-posedness of the proposed algorithm and its local superlinear convergence. The obtained results are also new for the class of equations defined by continuously differentiable functions with Lipschitzian derivatives ($\mathcal{C}^{1,1}$ functions), which is the underlying case of our consideration. The developed algorithm for prox-regular functions is formulated in terms of proximal mappings related to and reduces to Moreau envelopes. Besides numerous illustrative examples and comparison with known algorithms for $\mathcal{C}^{1,1}$ functions and generalized equations, the paper presents applications of the proposed algorithm to the practically important class of Lasso problems arising in statistics and machine learning.Comment: 35 page

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

Variational and Strong Variational Convexity in Infinite-Dimensional Variational Analysis

This paper is devoted to a systematic study and characterizations of the fundamental notions of variational and strong variational convexity for lower semicontinuous functions. While these notions have been quite recently introduced by Rockafellar, the importance of them has been already recognized and documented in finite-dimensional variational analysis and optimization. Here we address general infinite-dimensional settings and derive comprehensive characterizations of both variational and strong variational convexity notions by developing novel techniques, which are essentially different from finite-dimensional counterparts. As a consequence of the obtained characterizations, we establish new quantitative and qualitative relationships between strong variational convexity and tilt stability of local minimizers in appropriate frameworks of Banach spaces

Synthesis of Gold Nanobipyramids by Seed-mediated Method and Santibacterial Activities

Metallic nanoparticles as antibacterial agents have been studied for several years. The most used antibacterial nanoparticles are silver nanoparticles. The mechanisms and  antibacterial properties of silver nanoparticles are well known, but the effects of gold nanoparticles, especially gold Nano bipyramids, are not considered. In this research, we synthesized gold nanobipyramids (NBPs) by seed mediated method using surfactant cetyltrimethylammonium bromide (CTAB). After preparing, gold nanobipyramids is removed CTAB and modified the surface using polyethylene glycol, polyvinyl alcohol and chitosan as the stabilizers. Besides, antibacterial effects of gold nanobipyramids on both Escherichia coli (Gram negative) and Staphylococcus aureus (Gram positive) are investigated in this paper. The results show that gold nanobipyramids have good antibacterial activities even at low concentration. The optimal concentration of stabilizers and gold nanobipyramids in antibacterial activities are also studied in this paper

Cider Production from King Mandarin (Citrus nobilis Lour.) and Its Antioxidant Activity

With the necessity of diversifying alcoholic beverages, cider has become a kind of drink that can fulfill this demand. This is because the cider will be diversified depending on the kinds of fruit that are chosen to be used for the cider fermentation. Therefore, this study aims to investigate the effects of dilution ratio, Brix, pH, and yeast concentration on the production of cider from king mandarin (Citrus nobilis Lour.), and to evaluate the analytical characteristics and antioxidant activity of the product. After the investigation, it can be claimed that the dilution of the juice causes the ethanol content to decrease, whereas the increase of Brix, pH, and yeast concentration makes the ethanol content increase. However, the proportional increase in the ethanol content with Brix, pH, and yeast concentration has its limitations. Specifically, when the Brix and the yeast concentrations were, respectively, higher than 16°Brix and 0.04%, the ethanol content tended to maintain the same. This is also the same when the pH was lower than 4.5. In addition, by using the DPPH and ABTS●+ methods, the antioxidant activity of cider is estimated to be lower than the one of the juice before fermentation, which is smaller than 3.78 times for the DPPH method and 3.76 times for the ABTS●+ method

A Direct-Current Triboelectric Nanogenerator Energy Harvesting System Based on Water Electrification for Self-Powered Electronics

This study aimed to develop a simple but effective mechanical-to-electrical energy conversion for harvesting hydrokinetic energy based on triboelectric nanogenerator (TENG) technology. Here, a direct-current fluid-flow-based TENG is reported as a potential solution to solve the inconvenience of directly powering electronic devices where direct-current (DC) power is required. The falling of a water droplet (about 1.06 mL) from an elastomeric pipe can generate an open-circuit voltage of ~35 V, short-circuit current of 3.7 mu A, and peak power of 57.6 mu W by passing through a separated electrode. Notably, the electrical responses have the distinct characteristics of pulsed direct current. The ability to generate DC outputs enables the TENG to directly drive electronic devices. Our experimental results prove that this TENG can act as a power source to directly light up 50 light-emitting diodes without requiring a rectifier, and, also, the produced electric energy was demonstrated that can be stored directly in a capacitor to power commercial temperature and humidity IoT sensors. Furthermore, the device shows a greatly varied output voltage based on the droplet flow rate, with a linearity R-2 = 0.998. This work highlights a promising potential for applications in harvesting hydrokinetic energy and self-powered sensors and systems

Effect of leaching on shear strength of marine clay in Can Gio

Effect of leaching on shear strength of marine clay at Can Gio, Ho Chi Minh City is investigated in laboratory tests. Soil specimens were collected from three sites with different soil salinity. Testing includes shear strength and initial soil salinity. Leaching process is performed by modified equipment in laboratory with fresh water, then specimen is subjected to direct shear test to determine shear strength of leached and unleached soil. It is indicated that leaching affects the shear strength as reducing cohesion value (c, kPa) from 30% – 70% and internal friction angle (φ,o) from 8% - 20%

A Compact Adjustable Stiffness Rotary Actuator Based on Linear Springs: Working Principle, Design, and Experimental Verification

Inspired by improving the adaptive capability of the robot to external impacts or shocks, the adjustable stiffness behavior in joints is investigated to ensure conformity with the safety index. This paper proposes a new soft actuation unit, namely Adjustable Stiffness Rotary Actuator (ASRA), induced by a novel optimization of the elastic energy in an adjusting stiffness mechanism. Specifically, a stiffness transmission is configured by three pairs of antagonistically linear springs with linkage bars. The rotational disk and link bars assist the simplified stiffness control based on a linear transmission. To enhance the elastic energy efficiency, the force compressions of the linear springs are set to be perpendicular to the three-spoke output element, i.e., the output link direction. Besides, the ASRA model is also formed to investigate the theoretical capabilities of the stiffness output and passive energy. As a simulated result, a high passive energy storage ability can be achieved. Then, several experimental scenarios are performed with integral sliding mode controllers to verify the physical characteristics of the ASRA. As trial results, the fast transient response and high accuracy of both the position and stiffness tracking tests are expressed, in turn, independent and simultaneous control cases. Moreover, the real output torque is measured to investigate its reflecting stiffness