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This paper proposes an extended comparison principle for continuous-time linear positive time-delay systems. Unlike the existing comparison principle, which uses a constant initial function for the comparison system, instead, we propose a time-varying initial function in order to derive a more general solution comparison. Based on this extended comparison principle, we develop a novel computational method, which exploits more effectively the information of the initial value function, to derive tighter exponential estimates for the state vector of positive time-delay systems. The effectiveness of our developed method is illustrated through two numerical examples.

Long-pulsed 1064-nm (LP1064) and 755-nm (LP755) lasers have been demonstrated as effective treatments for leg veins. However, few studies of these treatments on Asian skin type as well as direct comparison between two methods were reported. The aim of this study was to compare the clinical efficacy and safety of LP1064 with LP755 in the treatment of C1 leg veins on skin type IV patients. Patients with symmetric matched areas C1 leg veins were treated with single session of LP1064 for the right and LP755 for the left. Treated areas of every patient were divided into matrices of 2 × 2 cm squares. Vessels in the highest density squares were subjected to evaluation. Spot sizes were 5 mm fixed. Pulse durations and fluences were according to vessel diameters and endpoints, respectively. The clearances were evaluated at 1 and 3 months post treatment. Side effects were recorded immediately, 10 min, 24 h, and 1 and 3 months after treatment. Twenty-two patients were enrolled with total 96 vessels from 22 selected squares in the right and 106 vessels from 22 selected squares in the left. At 1-month follow-up, the clearances of LP1064 and LP755 were not significantly different (71.87% and 71.69%, respectively; p = 0.99). At 3-month follow-up, the efficacies were constant and no recurrence occurred. Pain levels of both methods were moderate and significantly lower in LP755. These findings suggest that LP1064 and LP755 laser treatments were comparatively effective and safe for C1 leg veins of skin type IV patients.

Aims. This study is aimed at (1) validating the performance of Oakland and Glasgow-Blatchford (GBS) scores and (2) comparing these scores with the SALGIB score in predicting adverse outcomes of acute lower gastrointestinal bleeding (ALGIB) in a Vietnamese population. Methods. A multicenter cohort study was conducted on ALGIB patients admitted to seven hospitals across Vietnam. The adverse outcomes of ALGIB consisted of blood transfusion; endoscopic, radiologic, or surgical interventions; severe bleeding; and in-hospital death. The Oakland and GBS scores were calculated, and their performance was compared with that of SALGIB, a locally developed prediction score for adverse outcomes of ALGIB in Vietnamese, based on the data at admission. The accuracy of these scores was measured using the area under the receiver operating characteristic curve (AUC) and compared by the chi-squared test. Results. There were 414 patients with a median age of 60 (48–71). The rates of blood transfusion, hemostatic intervention, severe bleeding, and in-hospital death were 26.8%, 15.2%, 16.4, and 1.4%, respectively. The SALGIB score had comparable performance with the Oakland score (AUC: 0.81 and 0.81, respectively; p = 0.631 ) and outperformed the GBS score (AUC: 0.81 and 0.76, respectively; p = 0.002 ) for predicting the presence of any adverse outcomes of ALGIB. All of the three scores had acceptable and comparable performance for in-hospital death but poor performance for hemostatic intervention. The Oakland score had the best performance for predicting severe bleeding. Conclusions. The Oakland and SALGIB scores had excellent and comparable performance and outperformed the GBS score for predicting adverse outcomes of ALGIB in Vietnamese.

The prevalence of acute lower gastrointestinal bleeding (ALGIB) has progressively increased worldwide but there are few studies in Asian populations. This study aimed to develop and validate a scoring system to predict severe ALGIB in Vietnamese. Risk factors for severe ALGIB were identified by multiple logistic regression analysis using data from a retrospective cohort of 357 patients admitted to a tertiary hospital. These factors were weighted to develop the severe acute lower gastrointestinal bleeding (SALGIB) score to predict severe ALGIB. The performance of SALGIB was validated in a prospective cohort of 324 patients admitted to 6 other hospitals using area under the receiver operating characteristics curve (AUC) analysis. There were four factors at admission independently associated with severe ALGIB in the derivation cohort: heart rate ≥ 100/min, systolic blood pressure

We present a new method to find an α -exponential estimate for a class of positive discrete time-delay systems. Rather than finding an α -exponential estimate with a constant factor as in most of existing results, our novel idea is to find an α -exponential estimate with a decreasing factor function. As a result, we provide a smaller α -exponential estimate for the system. The effectiveness of the obtained result is illustrated through a numerical example.

To be able to compete in the domestic plastic industry, small and medium-sized enterprises producing plastic need to proactively find the supply of raw materials, avoiding shortages like in the previous years. Purchasing is extremely important and will create a competitive advantage with competitors in the market, so finding suppliers will determine the success in the later stages of the production chain. With the development of the current information system, selection and evaluation have become important in order to achieve effective decision-making through optimal options. In this study, the authors provide a new approach for decision-makers in evaluating and selecting suppliers, which is formulated based on the supply chain operation reference (SCOR) model, fuzzy analytic network process (FANP), and VIseKriterijumska Optimizacija I Kompromisno Resenje (VIKOR). The contribution of this research is to propose a multicriteria decision-making model (MCDM) for raw material supplier selection in the plastic industry. This research also provided a useful guideline for supplier selection in other industry.

University of Technology Sydney. Faculty of Science. A mix of evergreen rainforests and deciduous dry forests, the tropical forests in continental Southeast Asia (SEA) have been massively affected by human activities. Despite being highly threatened, very few studies have been conducted on SEA forests compared to the amount of studies conducted on their Amazonian and African counterparts. Consequently, studies on continental tropical forests in SEA need to be urgently conducted to gain a better understanding of their functioning and more specifically, their seasonal and inter-annual dynamics. Satellite data have proven useful in monitoring vegetated landscapes at variable spatial and temporal scales; however, variations of sun-sensor geometry have caused controversies over satellite-based results. Thus, the effect of variable sun-view angles on phenology needs to be investigated to minimise observation artefacts from real vegetation seasonal dynamics. The primary goal of this thesis is to study the inter- and intra-annual dynamics of continental SEA tropical forests using vegetation indices (VIs) derived from MODIS satellite data while also considering the effects of the bidirectional reflectance distribution function (BRDF) on the retrieved results. To achieve this goal, I first investigated continental SEA forest phenology and the effects of the BRDF on extracted phenological information. Next, I analysed the disturbance contribution in relation to intra-annual forest phenology by comparing seasonal profiles and phenological metrics between disturbed and undisturbed forests. Finally, I analysed the effects of the BRDF on the inter-annual VI variations and the inter-annual responses of SEA forests to climate variability. The results showed that the BRDF had substantial effects on the retrieved VI data. Thus, it appears that standardising reflectances and VIs at fixed sun-view angles is an essential process in the analysis of tropical forest phenology in the continental SEA region. Correcting the BRDF will prevent any unnecessary controversy in relation to the effects of varying illumination angles and the viewing geometries of satellite-based observations. Regarding the disturbance effects, my findings showed that disturbance affected SEA forest phenology in terms of both seasonal VI profiles and phenological metrics and that the BRDF correction helped to distinguish between disturbed and intact forests. My analyses also revealed that the inter-annual VI variations of SEA forests were affected by both the BRDF effect and climate variability. This thesis highlights the responses of continental SEA tropical forests to sun-angle geometries, climate seasonality and disturbances related to satellite observations. It makes an essential and significant contribution to understandings of SEA forest phenological diversity.

This thesis is devoted to the study of numerical algorithms for nonlinear optimization. On the one hand, we propose new strategies for the rapid infeasibility detection. On the other hand, we analyze the local behavior of primal-dual algorithms for the solution of singular problems. In the first part, we present a modification of an augmented Lagrangian algorithm for equality constrained optimization. The quadratic convergence of the new algorithm in the infeasible case is theoretically and numerically demonstrated. The second part is dedicated to extending the previous result to the solution of general nonlinear optimization problems with equality and inequality constraints. We propose a modification of a mixed logarithmic barrier-augmented Lagrangian algorithm. The theoretical convergence results and the numerical experiments show the advantage of the new algorithm for the infeasibility detection. In the third part, we study the local behavior of a primal-dual interior point algorithm for bound constrained optimization. The local analysis is done without the standard assumption of the second-order sufficient optimality conditions. These conditions are replaced by a weaker assumption based on a local error bound condition. We propose a regularization technique of the Jacobian matrix of the optimality system. We then demonstrate some boundedness properties of the inverse of these regularized matrices, which allow us to prove the superlinear convergence of our algorithm. The last part is devoted to the local convergence analysis of the primal-dual algorithm used in the first two parts of this thesis. In practice, it has been observed that this algorithm converges rapidly even in the case where the constraints do not satisfy the Mangasarian-Fromovitz constraint qualification. We demonstrate the superlinear and quadratic convergence of this algorithm without any assumption of constraint qualification.; Dans cette thèse, nous nous étudions des algorithmes d’optimisation non linéaire. D’une part nous proposons des techniques de détection rapide de la non-réalisabilité d’un problème à résoudre. D’autre part, nous analysons le comportement local des algorithmes pour la résolution de problèmes singuliers. Dans la première partie, nous présentons une modification d’un algorithme de lagrangien augmenté pour l’optimisation avec contraintes d’égalité. La convergence quadratique du nouvel algorithme dans le cas non-réalisable est démontrée théoriquement et numériquement. La seconde partie est dédiée à l’extension du résultat précédent aux problèmes d’optimisation non linéaire généraux avec contraintes d’égalité et d’inégalité. Nous proposons une modification d’un algorithme de pénalisation mixte basé sur un lagrangien augmenté et une barrière logarithmique. Les résultats théoriques de l’analyse de convergence et quelques tests numériques montrent l’avantage du nouvel algorithme dans la détection de la non-réalisabilité. La troisième partie est consacrée à étudier le comportement local d’un algorithme primal-dual de points intérieurs pour l’optimisation sous contraintes de borne. L’analyse locale est effectuée sans l’hypothèse classique des conditions suffisantes d’optimalité de second ordre. Celle-ci est remplacée par une hypothèse plus faible basée sur la notion de borne d’erreur locale. Nous proposons une technique de régularisation de la jacobienne du système d’optimalité à résoudre. Nous démontrons ensuite des propriétés de bornitude de l’inverse de ces matrices régularisées, ce qui nous permet de montrer la convergence superlinéaire de l’algorithme. La dernière partie est consacrée à l’analyse de convergence locale de l’algorithme primal-dual qui est utilisé dans les deux premières parties de la thèse. En pratique, il a été observé que cet algorithme converge rapidement même dans le cas où les contraintes ne vérifient l’hypothèse de qualification de Mangasarian-Fromovitz. Nous démontrons la convergence superlinéaire et quadratique de cet algorithme, sans hypothèse de qualification des contraintes.

We present a primal-dual augmented Lagrangian method for solving an equality constrained minimization problem, which is able to rapidly detect infeasibility. The method is based on a modification of the algorithm proposed in [1]. A new parameter is introduced to scale the objective function and, in case of infeasibility, to force the convergence of the iterates to an infea-sible stationary point. It is shown, under mild assumptions, that whenever the algorithm converges to an infeasible stationary point, the rate of convergence is quadratic. This is a new convergence result for the class of augmented La-grangian methods. The global convergence of the algorithm is also analysed. It is also proved that, when the algorithm converges to a stationary point, the properties of the original algorithm [1] are preserved. The numerical experiments show that our new approach is as good as the original one when the algorithm converges to a local minimum, but much more efficient in case of infeasibility.

We present a modification of a primal-dual algorithm [7] based on a mixed augmented Lagrangian and a log-barrier penalty function. The goal of this new feature is to quickly detect infeasibility. An additional parameter is introduced to balance the minimization of the objective function and the realization of the constraints. The rules of updating the parameters are based on [8]. The global convergence of the modified algorithm is analysed under mild assumptions. We also show that under a suitable choice of the parameters along the iterations, the rate of convergence of the algorithm to an infeasible stationary point is superlinear. This is the first local convergence result for the class of interior point methods in the infeasible case. We finally report some numerical experiments to show that this new algorithm is quite efficient to detect infeasibility and does not deteriorate the overall behavior in the general case.

This thesis is devoted to the study of numerical algorithms for nonlinear optimization. On the one hand, we propose new strategies for the rapid infeasibility detection. On the other hand, we analyze the local behavior of primal-dual algorithms for the solution of singular problems. In the first part, we present a modification of an augmented Lagrangian algorithm for equality constrained optimization. The quadratic convergence of the new algorithm in the infeasible case is theoretically and numerically demonstrated. The second part is dedicated to extending the previous result to the solution of general nonlinear optimization problems with equality and inequality constraints. We propose a modification of a mixed logarithmic barrier-augmented Lagrangian algorithm. The theoretical convergence results and the numerical experiments show the advantage of the new algorithm for the infeasibility detection. In the third part, we study the local behavior of a primal-dual interior point algorithm for bound constrained optimization. The local analysis is done without the standard assumption of the second-order sufficient optimality conditions. These conditions are replaced by a weaker assumption based on a local error bound condition. We propose a regularization technique of the Jacobian matrix of the optimality system. We then demonstrate some boundedness properties of the inverse of these regularized matrices, which allow us to prove the superlinear convergence of our algorithm. The last part is devoted to the local convergence analysis of the primal-dual algorithm used in the first two parts of this thesis. In practice, it has been observed that this algorithm converges rapidly even in the case where the constraints do not satisfy the Mangasarian-Fromovitz constraint qualification. We demonstrate the superlinear and quadratic convergence of this algorithm without any assumption of constraint qualification., Dans cette thèse, nous nous étudions des algorithmes d’optimisation non linéaire. D’une part nous proposons des techniques de détection rapide de la non-réalisabilité d’un problème à résoudre. D’autre part, nous analysons le comportement local des algorithmes pour la résolution de problèmes singuliers. Dans la première partie, nous présentons une modification d’un algorithme de lagrangien augmenté pour l’optimisation avec contraintes d’égalité. La convergence quadratique du nouvel algorithme dans le cas non-réalisable est démontrée théoriquement et numériquement. La seconde partie est dédiée à l’extension du résultat précédent aux problèmes d’optimisation non linéaire généraux avec contraintes d’égalité et d’inégalité. Nous proposons une modification d’un algorithme de pénalisation mixte basé sur un lagrangien augmenté et une barrière logarithmique. Les résultats théoriques de l’analyse de convergence et quelques tests numériques montrent l’avantage du nouvel algorithme dans la détection de la non-réalisabilité. La troisième partie est consacrée à étudier le comportement local d’un algorithme primal-dual de points intérieurs pour l’optimisation sous contraintes de borne. L’analyse locale est effectuée sans l’hypothèse classique des conditions suffisantes d’optimalité de second ordre. Celle-ci est remplacée par une hypothèse plus faible basée sur la notion de borne d’erreur locale. Nous proposons une technique de régularisation de la jacobienne du système d’optimalité à résoudre. Nous démontrons ensuite des propriétés de bornitude de l’inverse de ces matrices régularisées, ce qui nous permet de montrer la convergence superlinéaire de l’algorithme. La dernière partie est consacrée à l’analyse de convergence locale de l’algorithme primal-dual qui est utilisé dans les deux premières parties de la thèse. En pratique, il a été observé que cet algorithme converge rapidement même dans le cas où les contraintes ne vérifient l’hypothèse de qualification de Mangasarian-Fromovitz. Nous démontrons la convergence superlinéaire et quadratique de cet algorithme, sans hypothèse de qualification des contraintes.