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.      

Integration of an Equilibrium System in an Enhanced Theory of Bending of Elastic Plates

The complete integral of the system of partial differential equations governing the equilibrium bending of elastic plates with transverse shear deformation and transverse normal strain is constructed by means of complex variable methods. The process helps to elucidate the physical meaning of certain analytic constraints imposed on the asymptotic behavior of the solutions and shows that in the case of an infinite plate, any analytic solution has finite energy if and only if the bending and twisting moments, the transverse shear force, the displacements in vertical planes, and two other characteristic quantities vanish at infinity. An example is discussed to illustrate the theory.     

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.     

Vectorial penalization for generalized functional constrained problems

In this paper we use a double penalization procedure in order to reduce a set-valued optimization problem with functional constraints to an unconstrained one. The penalization results are given in several cases: for weak and strong solutions, in global and local settings, and considering two kinds of epigraphical mappings of the set-valued map that defines the constraints. Then necessary and sufficient conditions are obtained separately in terms of Bouligand derivatives of the objective and constraint mappings.     

On Some Methods to Derive Necessary and Sufficient Optimality Conditions in Vector Optimization

The aim of this paper is to address new approaches, in separate ways, to necessary and, respectively, sufficient optimality conditions in constrained vector optimization. In this respect, for the necessary optimality conditions that we derive, we use a kind of vectorial penalization technique, while for the sufficient optimality conditions we make use of an appropriate scalarization method. In both cases, the approaches couple a basic technique (of penalization or scalarization, respectively) with several results in variational analysis and optimization obtained by the authors in the last years. These combinations allow us to arrive to optimality conditions which are, in terms of assumptions made, new.     

A fluorescence anisotropy method for measuring protein concentration in complex cell culture media

The rapid, quantitative analysis of the complex cell culture media used in biopharmaceutical manufacturing is of critical importance. Requirements for cell culture media composition profiling, or changes in specific analyte concentrations (e.g. amino acids in the media or product protein in the bioprocess broth) often necessitate the use of complicated analytical methods and extensive sample handling. Rapid spectroscopic methods like multi-dimensional fluorescence (MDF) spectroscopy have been successfully applied for the routine determination of compositional changes in cell culture media and bioprocess broths. Quantifying macromolecules in cell culture media is a specific challenge as there is a need to implement measurements rapidly on the prepared media. However, the use of standard fluorescence spectroscopy is complicated by the emission overlap from many media components. Here, we demonstrate how combining anisotropy measurements with standard total synchronous fluorescence spectroscopy (TSFS) provides a rapid, accurate quantitation method for cell culture media. Anisotropy provides emission resolution between large and small fluorophores while TSFS provides a robust measurement space. Model cell culture media was prepared using yeastolate (2.5 mg mL^–1) spiked with bovine serum albumin (0 to 5 mg mL^–1). Using this method, protein emission is clearly discriminated from background yeastolate emission, allowing for accurate bovine serum albumin (BSA) quantification over a 0.1 to 4.0 mg mL^–1range with a limit of detection (LOD) of 13.8 μg mL^–1.     

On the convergence rate improvement of a primal-dual splitting algorithm for solving monotone inclusion problems

We present two modified versions of the primal-dual splitting algorithm relying on forward–backward splitting proposed in V\(\tilde{\mathrm{u}}\) (Adv Comput Math 38(3):667–681, 2013) for solving monotone inclusion problems. Under strong monotonicity assumptions for some of the operators involved we obtain for the sequences of iterates that approach the solution orders of convergence of \(\mathcal{{O}}(\frac{1}{n})\) and \(\mathcal{{O}}(\omega ^n)\), for \(\omega \in (0,1)\), respectively. The investigated primal-dual algorithms are fully decomposable, in the sense that the operators are processed individually at each iteration. We also discuss the modified algorithms in the context of convex optimization problems and present numerical experiments in image processing and pattern recognition in cluster analysis.     

Green light radiation effects on free radicals inhibition in cellular and chemical systems

Free radicals generation is inhibited through green light (GL) irradiation in cellular systems and in chemical reactions. Standard melanocyte cultures were UV-irradiated and the induced cellular reactive oxygen species (ROS) were quantified by the fluorescence technique. The same cell cultures, previously protected by a 24h GL exposure, displayed a significantly lower ROS production. A simple chemical reaction is subsequently chosen, in which the production of free radicals is well defined. Paraffin wax and mineral oil were GL irradiated during thermal degradation and the oxidation products checked by chemiluminescence [CL] and Fourier transform infrared spectra [FT-IR]. The same clear inhibition of the radical oxidation of alkanes is recorded. A quantum chemistry modeling of these results is performed and a mechanism involving a new type of Rydberg macromolecular systems with implications for biology and medicine is suggested.