Duality for location problems with unbounded unit balls

Given an optimization problem with a composite of a convex and componentwise increasing function with a convex vector function as objective function, by means of the conjugacy approach based on the perturbation theory, we determine a dual to it. Necessary and sufficient optimality conditions are derived using strong duality. Furthermore, as special case of this problem, we consider a location problem, where the “distances” are measured by gauges of closed convex sets. We prove that the geometric characterization of the set of optimal solutions for this location problem given by Hinojosa and Puerto in a recently published paper can be obtained via the presented dual problem. Finally, the Weber and the minmax location problems with gauges are given as applications.     

Comparison between different duals in multiobjective fractional programming

The present paper is a continuation of [2] where we deal with the duality for a multiobjective fractional optimization problem. The basic idea in [2] consists in attaching an intermediate multiobjective convex optimization problem to the primal fractional problem, using an approach due to Dinkelbach ([6]), for which we construct then a dual problem expressed in terms of the conjugates of the functions involved. The weak, strong and converse duality statements for the intermediate problems allow us to give dual characterizations for the efficient solutions of the initial fractional problem. The aim of this paper is to compare the intermediate dual problem with other similar dual problems known from the literature. We completely establish the inclusion relations between the image sets of the duals as well as between the sets of maximal elements of the image sets.      

High frequency parallel plate probe for the measurement of the complex viscosity of liquids

In this work an instrument is described which measures the complex shear viscosity of liquids in the kHz frequency range. The instrument is driven electromagnetically and operates in resonant mode. The measurement of the primary data, from which the rheological properties of the fluid sample are inferred, does not include any deflection amplitude measuring step and is purely digital. Models allowing the interpretation of the probe primary data in terms of fluid complex viscosity are presented. The theoretically predicted mechanical behaviour of the probe is compared with the measured one and the rheometric ability of the device is discussed.     

Ambazone salt with p-aminobenzoic acid

In this study, we obtained a novel salt of ambazone (AMB) with p-aminobenzoic acid (PABA) that exhibits improved solubility and antibacterial activity. The salt was produced by solvent-drop grinding and characterized by powder X-ray diffraction, thermal analysis and Fourier transform infrared spectroscopy. The salt nature of the new form was confirmed by infrared spectroscopy based on the characteristic vibrational band of the protonated amino group. Based on the X-ray powder diffraction data, the compound crystallizes in the triclinic P_-1 space group with the following unit cell parameters: a = 14.294 Å, b = 9.162 Å, c = 8.777 Å, α = 95.90°, β = 100.63°, γ = 91.73°. Thermal analysis reveals the thermal events and different decomposition steps of this solid form as compared to the starting compounds. Powder dissolution measurements showed solubility improvement compared with pure ambazone of 2 and 3.3 times in water and phosphate buffer, respectively. Antibacterial tests showed higher activity of the salt to Gram-negative Escherichia coli and Salmonella bacteria as compared to AMB and PABA. The study demonstrates that the pharmaceutical salt of ambazone with p-aminobenzoic acid (AMB–PABA) can be a possible alternative to ambazone in the treatment of infections with Gram-negative bacteria.     

Proximal-gradient algorithms for fractional programming

In this paper, we propose two proximal-gradient algorithms for fractional programming problems in real Hilbert spaces, where the numerator is a proper, convex and lower semicontinuous function and the denominator is a smooth function, either concave or convex. In the iterative schemes, we perform a proximal step with respect to the nonsmooth numerator and a gradient step with respect to the smooth denominator. The algorithm in case of a concave denominator has the particularity that it generates sequences which approach both the (global) optimal solutions set and the optimal objective value of the underlying fractional programming problem. In case of a convex denominator the numerical scheme approaches the set of critical points of the objective function, provided the latter satisfies the Kurdyka-?ojasiewicz property.