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

ASSESSING THE POTENTIAL OF COMMUNITY-BASED ECOTOURISM TOWARD SUSTAINABLE DEVELOPMENT: A CASE STUDY IN TUA CHUA KARST PLATEAU – DIEN BIEN – VIET NAM

Tua Chua Karst Plateau - a living area of the Mong ethnic group with spectacular natural landscapes, cool weather, and unique indigenous cultural values. They are all prerequisites for tourism development. This study aims to evaluate the potential of community-based ecotourism development in the Tua Chua Karst Plateau. This research uses the AHP method. Evaluation criteria include (i) uniqueness of natural landscape, (ii) indigenous cultural value, (iii) stakeholder engagement, (iv) local tourism development policy, (v) quality of infrastructure, (vi) quality of tourism facilities, (vii) accessibility, (viii) connectivity. The evaluation system includes eight criteria that have classified tourism resources according to each resource point and identified suitable internal and external potentials to exploit the geological value of the plateau and preserve indigenous culture. Results of this study reveal that the indigenous cultural values, the participation of local communities, and the uniqueness of the natural landscape have an important impact on the development of ecotourism. Tua Chua Karst Plateau has great potential for community-based ecotourism development with 14 tourist resource sites, of which 8 are highly appreciated

The acceptance of mobile applications for accommodation booking in Vietnam: Case of gen Z

The development of technology and smart mobile devices such as phones and tablets has changed the behavior of tourists when booking tourism services. Based on the technology acceptance model, this study aims to explore the factors influencing the intention to use mobile applications for accommodation booking among GENZ in Vietnam. The analysis of 218 users revealed that four factors influence the behavior of using mobile applications for booking: performance expectancy, effort expectancy, social influence, and hedonic motivation. In addition to identifying the factors affecting usage intention, this study also proposes implications to assist developers and providers in improving their applications and developing suitable product strategies for the future

Study on total lipid content, lipid class composition of some fire and soft corals collected in Nha Trang, Vietnam

For the first time, the total lipid content and lipid class composition of  the Vietnamese soft corals (Sinularia brassica, Sinularia flexibilis) and fire corals (Millepora dichotoma, Millepora platyphylla) were investigated. The results indicated that the total lipid content of the investigated species was significantly different. Compositions of the lipid classes were analyzed using TLC and image analysis program Sorbfil TLC Videodensitometer DV and the results showed that phospholipids (PL, 10.91–16.02%), monoalkyldiacylglycerols (MADAG, 20.69-39.92%) and hydrocarbon wax (HW, 29.83-37.17%) were the main lipid classes of the total lipid in soft coral species. Meanwhile, PL (24.11-33.23%), TG (14.27–34.92%), ST (10.10–14.50%) and HW (12.08–19.95%) were predominant in fire coral species. ST, TG and FFA contents in soft and fire corals were at low level. DG was only present in the Sinularia flexibilis but not in other studied corals

Phylogeographical analysis of the dominant multidrug-resistant H58 clade of Salmonella Typhi identifies inter- and intracontinental transmission events.

The emergence of multidrug-resistant (MDR) typhoid is a major global health threat affecting many countries where the disease is endemic. Here whole-genome sequence analysis of 1,832 Salmonella enterica serovar Typhi (S. Typhi) identifies a single dominant MDR lineage, H58, that has emerged and spread throughout Asia and Africa over the last 30 years. Our analysis identifies numerous transmissions of H58, including multiple transfers from Asia to Africa and an ongoing, unrecognized MDR epidemic within Africa itself. Notably, our analysis indicates that H58 lineages are displacing antibiotic-sensitive isolates, transforming the global population structure of this pathogen. H58 isolates can harbor a complex MDR element residing either on transmissible IncHI1 plasmids or within multiple chromosomal integration sites. We also identify new mutations that define the H58 lineage. This phylogeographical analysis provides a framework to facilitate global management of MDR typhoid and is applicable to similar MDR lineages emerging in other bacterial species

Safety and efficacy of fluoxetine on functional outcome after acute stroke (AFFINITY): a randomised, double-blind, placebo-controlled trial

Background Trials of fluoxetine for recovery after stroke report conflicting results. The Assessment oF FluoxetINe In sTroke recoverY (AFFINITY) trial aimed to show if daily oral fluoxetine for 6 months after stroke improves functional outcome in an ethnically diverse population. Methods AFFINITY was a randomised, parallel-group, double-blind, placebo-controlled trial done in 43 hospital stroke units in Australia (n=29), New Zealand (four), and Vietnam (ten). Eligible patients were adults (aged ≥18 years) with a clinical diagnosis of acute stroke in the previous 2–15 days, brain imaging consistent with ischaemic or haemorrhagic stroke, and a persisting neurological deficit that produced a modified Rankin Scale (mRS) score of 1 or more. Patients were randomly assigned 1:1 via a web-based system using a minimisation algorithm to once daily, oral fluoxetine 20 mg capsules or matching placebo for 6 months. Patients, carers, investigators, and outcome assessors were masked to the treatment allocation. The primary outcome was functional status, measured by the mRS, at 6 months. The primary analysis was an ordinal logistic regression of the mRS at 6 months, adjusted for minimisation variables. Primary and safety analyses were done according to the patient's treatment allocation. The trial is registered with the Australian New Zealand Clinical Trials Registry, ACTRN12611000774921. Findings Between Jan 11, 2013, and June 30, 2019, 1280 patients were recruited in Australia (n=532), New Zealand (n=42), and Vietnam (n=706), of whom 642 were randomly assigned to fluoxetine and 638 were randomly assigned to placebo. Mean duration of trial treatment was 167 days (SD 48·1). At 6 months, mRS data were available in 624 (97%) patients in the fluoxetine group and 632 (99%) in the placebo group. The distribution of mRS categories was similar in the fluoxetine and placebo groups (adjusted common odds ratio 0·94, 95% CI 0·76–1·15; p=0·53). Compared with patients in the placebo group, patients in the fluoxetine group had more falls (20 [3%] vs seven [1%]; p=0·018), bone fractures (19 [3%] vs six [1%]; p=0·014), and epileptic seizures (ten [2%] vs two [<1%]; p=0·038) at 6 months. Interpretation Oral fluoxetine 20 mg daily for 6 months after acute stroke did not improve functional outcome and increased the risk of falls, bone fractures, and epileptic seizures. These results do not support the use of fluoxetine to improve functional outcome after stroke

Factors impact on customers behaviour on the choice of independent coffee shops

The research is focused on factors affect to the behaviour and satisfaction of customer on the choice of coffee shops. Some factors such as price, quality, taste, locations, and additional factors have been mentioned in this research to attract customers. The study is only about independent coffee shops. The research has conducted a questionnaire. There are 200 respondents has been taken and 164 valid results which have been chosen for analysis. There are some trends has been shown in the study. The quality of service is the factors that most of people think it is very important when visit independent coffee shops then the followings are friendly staff, location and quality of coffee while majority of respondents chose music is not important factor. This study found, culture does not affect on price, quality of service and taste. This study also found people above 31 years old tend to support local business while more people from 18-30 visit independent coffee shops because of Wifi accessibility, value for money and reputation reason