Fundamental qualitative properties of the minimum sum-of-squares clustering problem are established in this paper. We prove that the problem always has a global solution and, under a mild condition, ...the global solution set is finite. Moreover, the components of each global solution can be computed by an explicit formula. Based on a new concept of non-trivial local solution, we get necessary conditions for a system of centroids to be such a local solution. Interestingly, these necessary conditions are also sufficient ones. Finally, it is proved that the optimal value function is locally Lipschitz, the global solution map is locally upper Lipschitz, and the local solution map has the Aubin property, provided that the original data points are distinct. The obtained complete characterizations of the non-trivial local solutions allow one to understand better the performance of not only the k-means algorithm, but also of other solution methods for the problem in question.
We establish some properties of the Proximal Difference-of-Convex functions decomposition algorithm in indefinite quadratic programming under linear constraints. The first property states that any ...iterative sequence generated by the algorithm is root linearly convergent to a Karush-Kuhn-Tucker point, provided that the problem has a solution. The second property says that iterative sequences generated by the algorithm converge to a locally unique solution of the problem if the initial points are taken from a suitably chosen neighbourhood of it. Through a series of numerical tests, we analyse the influence of the decomposition parameter on the rate of convergence of the iterative sequences and compare the performance of the Proximal Difference-of-Convex functions decomposition algorithm with that of the Projection Difference-of-Convex functions decomposition algorithm. In addition, the performances of the above algorithms and the Gurobi software in solving some randomly generated nonconvex quadratic programs are compared.
We consider the conic linear program given by a closed convex cone in an Euclidean space and a matrix, where vector on the right-hand side of the inequality constraint and the vector defining the ...objective function are subject to change. Using the strict feasibility condition, we prove the locally Lipschitz continuity and obtain some differentiability properties of the optimal value function of the problem under right-hand-side perturbations. For the optimal value function under linear perturbations of the objective function, similar differentiability properties are obtained under the assumption saying that both primal problem and dual problem are strictly feasible.
This paper studies infinite-dimensional affine variational inequalities on normed spaces. It is shown that infinite-dimensional quadratic programming problems and infinite-dimensional linear ...fractional vector optimization problems can be studied by using affine variational inequalities. We present two basic facts about infinite-dimensional affine variational inequalities: the Lagrange multiplier rule and the solution set decomposition.
It is well known that finite-dimensional polyhedral convex sets can be generated by finitely many points and finitely many directions. Representation formulas in this spirit are obtained for convex ...polyhedra and generalized convex polyhedra in locally convex Hausdorff topological vector spaces. Our results develop those of X. Y. Zheng (Set-Valued Anal. 2009;17:389-408), which were established in a Banach space setting. Applications of the representation formulas to proving solution existence theorems for generalized linear programming problems and generalized linear vector optimization problems are shown.
Improperly efficient solutions in the sense of Geoffrion in linear fractional vector optimization problems with unbounded constraint sets are studied systematically for the first time in this paper. ...We give two sets of conditions which assure that all the efficient solutions of a given problem are improperly efficient. We also obtain necessary conditions for an efficient solution to be improperly efficient. As a result, we have new sufficient conditions for Geoffrion’s proper efficiency. The obtained results enrich our knowledge on properly efficient solutions in linear fractional vector optimization.
This paper gives some results related to the research problem about infinite-dimensional affine variational inequalities raised by N.D. Yen and X. Yang Affine variational inequalities on normed ...spaces, J. Optim. Theory Appl. 178 (2018), 36-55. Namely, we obtain local error bounds for affine variational inequalities on Hilbert spaces. To do so, we revisit two fundamental properties of polyhedral mappings. Then, we prove a locally upper Lipschitz property of the inverse of the residual mapping of the infinite-dimensional affine variational inequality under consideration. Finally, we derive the desired local error bounds from that locally upper Lipschitz property.
Quercetin has been studied extensively with drug delivery systems due to the drug's needs to improve in solubility, but usually the systems are complicated, evading the practical aspects and ...potential applications. This problem is expected to be solved using the simplistic micelles, in combination with the materials mPEG and cholesterol to gain advantages from the nano‐size, while increasing its overall stability and drug releasing. In this study PEGylated‐cholesterol micelles were prepared by co‐solvent method in 4 different drug‐polymer ratios, which were then characterized by physical–chemical, in vitro analyses and emphasized on the in vivo cytotoxicity test by H&E staining histological assay on Danio rerio model. The results show promising features of nano‐micelles as a passive drug delivery system in size, CMC value, and prolonged drug releasing profile. Compared to free QCT, the micelles‐loaded system exhibited significantly higher toxicity in vitro, which were also demonstrated in in vivo models, where the drug‐loaded micellar systems posed mild tissue changes, while blank micelles and free quercetin were almost harmless to the animals. The results had concluded that effective delivering of micellar system does not require advanced material‐composition, rather a throughout understanding of the interactions of nano‐properties and the materials with bio‐systems.
Quercetin drugs were incorporated in the hydrophobic inner‐section of micellar particles, and the weight ratio between these were examined to optimize the drug‐loading capacity. The micellar nanoparticles were then subject to various analytical experiments, which provide sufficient data about “drug‐delivering” ability of mPEG‐Cholesterol as materials for micelles’ formulations. With the increase in requirements for in vivo tests recently and the limited properties of rodent and mammal models, we have developed a testing protocol using zebrafish (Danio rerio) models to examine in vivo the anti‐cancer drug’ effect on bodily systems.
We study a class of finite horizon optimal economic growth problems with nonlinear utility functions and linear production functions. By using a maximum principle in the optimal control theory and ...employing the special structure of the problems, we are able to explicitly describe the unique solution via input parameters. Economic interpretations of the obtained results and an open problem about the case where the total factor productivity falls into a bounded open interval defined by the growth rate of labor force, the real interest rate, and the exponent of the utility function are also expressed.
We investigated antimicrobial residues, non-typhoidal Salmonella (NTS), Vibrio spp. and their associated antimicrobial resistance (AMR), in shrimps locally purchased in Ho Chi Minh City (Vietnam). In ...addition, we investigated the relationship between AMR in NTS, Vibrio spp. and antimicrobial residue in the same sample. A total of 40 samples of shrimp heads/shells from different retail sources was cultured using ISO 6579–1:2017 (NTS) and ISO/TS 21872–1:2007 (Vibrio spp.). Phenotypic antimicrobial susceptibility was investigated using Vitek (NTS, 34 antimicrobials) and disk diffusion (Vibrio spp., 12 antimicrobials). A total of 9 (22.5%) samples contained antimicrobial residue, including tetracyclines, fluoroquinolones, sulfonamides and macrolides (in 7.5%, 7.5%, 2.5% and 2.5% of samples, respectively). Shrimp samples from supermarkets had a higher prevalence of antimicrobial residue than those purchased in street markets (50% vs. 13.3%) (p = 0.049). A total of 30 (75%) samples were contaminated with NTS. All samples contained Vibrio spp., with V. parahaemolyticus being most common (87.5% samples). A total of 58.9% NTS isolates were multidrug resistant. With regards to the highest priority, critically important antimicrobials, the highest resistance corresponded to quinolones (14.4–47.8%), followed by 3rd and 4th generation cephalosporins (3.3–7.8%). Vibrio spp. isolates were characterised by their high resistance against ampicillin (82.7%) and 3rd generation cephalosporins (8.3–16.5%). Extended Spectrum Beta-Lactamase (ESBL) activity was detected in 28.1% V. parahaemolyticus isolates. Half of ESBL-positive V. parahaemolyticus strains harboured blaCTX-M1. We found an association between the presence of residues and the number of resistances for NTS (p = 0.075) and Vibrio spp. isolates (p = 0.093) from the same sample. These findings suggest that the presence of residues may contribute to the selection of AMR in foodborne pathogens in shrimps. Authorities should strengthen policies aiming at restricting inappropriate antimicrobial usage in shrimp farming, and step up monitoring of antimicrobial residues and food-borne pathogens at retail in Vietnam.
•Highest prevalence of antimicrobial residues found in shrimps from supermarkets.•75% samples were contaminated with non-typhoidal Salmonella (NTS).•Isolates from samples with antimicrobial residues had highest prevalence of phenotypic resistance.•Extended Spectrum Beta-Lactamase activity detected in 28.1% V. parahaemolyticus isolates.
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